Quadratic equations for math practice.

You've uploaded a math worksheet titled “Math Practice” with six quadratic equations to solve. All are in standard form:
> ax² + bx + c = 0

We’ll solve each using factoring, since all appear factorable (as is common in practice worksheets). Let’s go one by one.

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🔹 Equation 1:

2x² – 2x – 24 = 0

✔ Step 1: Factor out the GCF (Greatest Common Factor)
All terms divisible by 2 →
→ 2(x² – x – 12) = 0

✔ Step 2: Factor the trinomial
We need two numbers that multiply to –12 and add to –1:
→ –4 and +3

So:
→ 2(x – 4)(x + 3) = 0

✔ Step 3: Set each factor = 0
→ x – 4 = 0 → x = 4
→ x + 3 = 0 → x = –3

✔ Solutions: x = 4, x = –3

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🔹 Equation 2:

x² + 10x + 16 = 0

✔ Find two numbers that multiply to 16 and add to 10:
→ 8 and 2

→ (x + 8)(x + 2) = 0

✔ Solutions:
→ x + 8 = 0 → x = –8
→ x + 2 = 0 → x = –2

✔ Solutions: x = –8, x = –2

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🔹 Equation 3:

4x² + 15x + 9 = 0

✔ Need two numbers that multiply to 4×9 = 36 and add to 15 → 12 and 3

Rewrite middle term:
→ 4x² + 12x + 3x + 9 = 0

Group:
→ (4x² + 12x) + (3x + 9) = 0
→ 4x(x + 3) + 3(x + 3) = 0
→ (4x + 3)(x + 3) = 0

✔ Solutions:
→ 4x + 3 = 0 → x = –3/4
→ x + 3 = 0 → x = –3

✔ Solutions: x = –3/4, x = –3

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🔹 Equation 4:

x² – 13x + 42 = 0

✔ Two numbers that multiply to 42 and add to –13:
→ –6 and –7

→ (x – 6)(x – 7) = 0

✔ Solutions:
→ x – 6 = 0 → x = 6
→ x – 7 = 0 → x = 7

✔ Solutions: x = 6, x = 7

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🔹 Equation 5:

6x² – x – 40 = 0

✔ Multiply a×c = 6×(–40) = –240
Need two numbers that multiply to –240 and add to –1 → –16 and +15

Rewrite:
→ 6x² – 16x + 15x – 40 = 0

Group:
→ (6x² – 16x) + (15x – 40) = 0
→ 2x(3x – 8) + 5(3x – 8) = 0
→ (2x + 5)(3x – 8) = 0

✔ Solutions:
→ 2x + 5 = 0 → x = –5/2
→ 3x – 8 = 0 → x = 8/3

✔ Solutions: x = –5/2, x = 8/3

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🔹 Equation 6:

2x² + 13x + 15 = 0

✔ Multiply a×c = 2×15 = 30
Need two numbers that multiply to 30 and add to 13 → 10 and 3

Rewrite:
→ 2x² + 10x + 3x + 15 = 0

Group:
→ (2x² + 10x) + (3x + 15) = 0
→ 2x(x + 5) + 3(x + 5) = 0
→ (2x + 3)(x + 5) = 0

✔ Solutions:
→ 2x + 3 = 0 → x = –3/2
→ x + 5 = 0 → x = –5

✔ Solutions: x = –3/2, x = –5

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## ✔ Final Answers:

| Equation | Solutions |
|----------|---------|
| 2x² – 2x – 24 = 0 | x = 4, x = –3 |
| x² + 10x + 16 = 0 | x = –8, x = –2 |
| 4x² + 15x + 9 = 0 | x = –3/4, x = –3 |
| x² – 13x + 42 = 0 | x = 6, x = 7 |
| 6x² – x – 40 = 0 | x = –5/2, x = 8/3 |
| 2x² + 13x + 15 = 0 | x = –3/2, x = –5 |

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Let me know if you’d like to see these solved using the quadratic formula or graphed!