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Simplifying (9x + -7)(6x + 6) = 0 Reorder the terms: (-7 + 9x)(6x + 6) = 0 Reorder the terms: (-7 + 9x)(6 + 6x) = 0 Multiply (-7 + 9x) * (6 + 6x) (-7(6 + 6x) + 9x * (6 + 6x)) = 0 ((6 * -7 + 6x * -7) + 9x * (6 + 6x)) = 0 ((-42 + -42x) + 9x * (6 + 6x)) = 0 (-42 + -42x + (6 * 9x + 6x * 9x)) = 0 (-42 + -42x + (54x + 54x2)) = 0 Combine like terms: -42x + 54x = 12x (-42 + 12x + 54x2) = 0 Solving -42 + 12x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-7 + 2x + 9x2) = 0 Factor a trinomial. 6((-1 + -1x)(7 + -9x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(7 + -9x)' equal to zero and attempt to solve: Simplifying 7 + -9x = 0 Solving 7 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -9x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9x = 0 + -7 -9x = 0 + -7 Combine like terms: 0 + -7 = -7 -9x = -7 Divide each side by '-9'. x = 0.7777777778 Simplifying x = 0.7777777778Solution
x = {-1, 0.7777777778}
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