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Simplifying (2x + -7)(9x + 6) = 0 Reorder the terms: (-7 + 2x)(9x + 6) = 0 Reorder the terms: (-7 + 2x)(6 + 9x) = 0 Multiply (-7 + 2x) * (6 + 9x) (-7(6 + 9x) + 2x * (6 + 9x)) = 0 ((6 * -7 + 9x * -7) + 2x * (6 + 9x)) = 0 ((-42 + -63x) + 2x * (6 + 9x)) = 0 (-42 + -63x + (6 * 2x + 9x * 2x)) = 0 (-42 + -63x + (12x + 18x2)) = 0 Combine like terms: -63x + 12x = -51x (-42 + -51x + 18x2) = 0 Solving -42 + -51x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + -17x + 6x2) = 0 Factor a trinomial. 3((-2 + -3x)(7 + -2x)) = 0 Ignore the factor 3.Subproblem 1
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 = -0.6666666667Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {-0.6666666667, 3.5}
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