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Simplifying (6x + -12)(x + 17) = 0 Reorder the terms: (-12 + 6x)(x + 17) = 0 Reorder the terms: (-12 + 6x)(17 + x) = 0 Multiply (-12 + 6x) * (17 + x) (-12(17 + x) + 6x * (17 + x)) = 0 ((17 * -12 + x * -12) + 6x * (17 + x)) = 0 ((-204 + -12x) + 6x * (17 + x)) = 0 (-204 + -12x + (17 * 6x + x * 6x)) = 0 (-204 + -12x + (102x + 6x2)) = 0 Combine like terms: -12x + 102x = 90x (-204 + 90x + 6x2) = 0 Solving -204 + 90x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-34 + 15x + x2) = 0 Factor a trinomial. 6((-17 + -1x)(2 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve: Simplifying -17 + -1x = 0 Solving -17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x = 0 + 17 -1x = 0 + 17 Combine like terms: 0 + 17 = 17 -1x = 17 Divide each side by '-1'. x = -17 Simplifying x = -17Subproblem 2
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 = 2Solution
x = {-17, 2}
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