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Simplifying (9x + -6)(7x + 7) = 0 Reorder the terms: (-6 + 9x)(7x + 7) = 0 Reorder the terms: (-6 + 9x)(7 + 7x) = 0 Multiply (-6 + 9x) * (7 + 7x) (-6(7 + 7x) + 9x * (7 + 7x)) = 0 ((7 * -6 + 7x * -6) + 9x * (7 + 7x)) = 0 ((-42 + -42x) + 9x * (7 + 7x)) = 0 (-42 + -42x + (7 * 9x + 7x * 9x)) = 0 (-42 + -42x + (63x + 63x2)) = 0 Combine like terms: -42x + 63x = 21x (-42 + 21x + 63x2) = 0 Solving -42 + 21x + 63x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '21'. 21(-2 + x + 3x2) = 0 Factor a trinomial. 21((-1 + -1x)(2 + -3x)) = 0 Ignore the factor 21.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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-1, 0.6666666667}
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