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Simplifying 0 = 6x2 + -102x + 432 Reorder the terms: 0 = 432 + -102x + 6x2 Solving 0 = 432 + -102x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -432 = -432 -432 + 102x + -6x2 = 432 + -102x + 6x2 + -432 + 102x + -6x2 Reorder the terms: -432 + 102x + -6x2 = 432 + -432 + -102x + 102x + 6x2 + -6x2 Combine like terms: 432 + -432 = 0 -432 + 102x + -6x2 = 0 + -102x + 102x + 6x2 + -6x2 -432 + 102x + -6x2 = -102x + 102x + 6x2 + -6x2 Combine like terms: -102x + 102x = 0 -432 + 102x + -6x2 = 0 + 6x2 + -6x2 -432 + 102x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -432 + 102x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-72 + 17x + -1x2) = 0 Factor a trinomial. 6((-9 + x)(8 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {9, 8}
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