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Simplifying 6(x + 2)(x + -3) = 0 Reorder the terms: 6(2 + x)(x + -3) = 0 Reorder the terms: 6(2 + x)(-3 + x) = 0 Multiply (2 + x) * (-3 + x) 6(2(-3 + x) + x(-3 + x)) = 0 6((-3 * 2 + x * 2) + x(-3 + x)) = 0 6((-6 + 2x) + x(-3 + x)) = 0 6(-6 + 2x + (-3 * x + x * x)) = 0 6(-6 + 2x + (-3x + x2)) = 0 Combine like terms: 2x + -3x = -1x 6(-6 + -1x + x2) = 0 (-6 * 6 + -1x * 6 + x2 * 6) = 0 (-36 + -6x + 6x2) = 0 Solving -36 + -6x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-6 + -1x + x2) = 0 Factor a trinomial. 6((-2 + -1x)(3 + -1x)) = 0 Ignore the factor 6.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 = -2Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-2, 3}
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