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Simplifying (5x + -6)(9x + 6) = 0 Reorder the terms: (-6 + 5x)(9x + 6) = 0 Reorder the terms: (-6 + 5x)(6 + 9x) = 0 Multiply (-6 + 5x) * (6 + 9x) (-6(6 + 9x) + 5x * (6 + 9x)) = 0 ((6 * -6 + 9x * -6) + 5x * (6 + 9x)) = 0 ((-36 + -54x) + 5x * (6 + 9x)) = 0 (-36 + -54x + (6 * 5x + 9x * 5x)) = 0 (-36 + -54x + (30x + 45x2)) = 0 Combine like terms: -54x + 30x = -24x (-36 + -24x + 45x2) = 0 Solving -36 + -24x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + -8x + 15x2) = 0 Factor a trinomial. 3((-2 + -3x)(6 + -5x)) = 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 '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2Solution
x = {-0.6666666667, 1.2}
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