QuestionJuly 15, 2025

Use factoring to solve the polynomial equation: x(x-3)=2(x+12) Answer: square

Use factoring to solve the polynomial equation: x(x-3)=2(x+12) Answer: square
Use factoring to solve the polynomial equation:
x(x-3)=2(x+12)
Answer: square

Solution
4.4(341 votes)

Answer

x = 8, -3 Explanation 1. Expand the equation Distribute both sides: x^2 - 3x = 2x + 24. 2. Rearrange terms Move all terms to one side: x^2 - 3x - 2x - 24 = 0, simplifying to x^2 - 5x - 24 = 0. 3. Factor the quadratic Find factors of -24 that add up to -5: (x - 8)(x + 3) = 0. 4. Solve for x Set each factor to zero: x - 8 = 0 or x + 3 = 0.

Explanation

1. Expand the equation<br /> Distribute both sides: $x^2 - 3x = 2x + 24$.<br />2. Rearrange terms<br /> Move all terms to one side: $x^2 - 3x - 2x - 24 = 0$, simplifying to $x^2 - 5x - 24 = 0$.<br />3. Factor the quadratic<br /> Find factors of $-24$ that add up to $-5$: $(x - 8)(x + 3) = 0$.<br />4. Solve for x<br /> Set each factor to zero: $x - 8 = 0$ or $x + 3 = 0$.
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