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Simplifying (12x + 4)(13x + -5) = 0 Reorder the terms: (4 + 12x)(13x + -5) = 0 Reorder the terms: (4 + 12x)(-5 + 13x) = 0 Multiply (4 + 12x) * (-5 + 13x) (4(-5 + 13x) + 12x * (-5 + 13x)) = 0 ((-5 * 4 + 13x * 4) + 12x * (-5 + 13x)) = 0 ((-20 + 52x) + 12x * (-5 + 13x)) = 0 (-20 + 52x + (-5 * 12x + 13x * 12x)) = 0 (-20 + 52x + (-60x + 156x2)) = 0 Combine like terms: 52x + -60x = -8x (-20 + -8x + 156x2) = 0 Solving -20 + -8x + 156x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -2x + 39x2) = 0 Factor a trinomial. 4((-1 + -3x)(5 + -13x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
Set the factor '(5 + -13x)' equal to zero and attempt to solve: Simplifying 5 + -13x = 0 Solving 5 + -13x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -13x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -13x = 0 + -5 -13x = 0 + -5 Combine like terms: 0 + -5 = -5 -13x = -5 Divide each side by '-13'. x = 0.3846153846 Simplifying x = 0.3846153846Solution
x = {-0.3333333333, 0.3846153846}
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