-2(x-2)(x+3)=0

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Solution for -2(x-2)(x+3)=0 equation:


Simplifying
-2(x + -2)(x + 3) = 0

Reorder the terms:
-2(-2 + x)(x + 3) = 0

Reorder the terms:
-2(-2 + x)(3 + x) = 0

Multiply (-2 + x) * (3 + x)
-2(-2(3 + x) + x(3 + x)) = 0
-2((3 * -2 + x * -2) + x(3 + x)) = 0
-2((-6 + -2x) + x(3 + x)) = 0
-2(-6 + -2x + (3 * x + x * x)) = 0
-2(-6 + -2x + (3x + x2)) = 0

Combine like terms: -2x + 3x = 1x
-2(-6 + 1x + x2) = 0
(-6 * -2 + 1x * -2 + x2 * -2) = 0
(12 + -2x + -2x2) = 0

Solving
12 + -2x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -1x + -1x2) = 0

Factor a trinomial.
2((2 + -1x)(3 + x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {2, -3}

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