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Simplifying 5(6x + -7)(2x + 5) = 0 Reorder the terms: 5(-7 + 6x)(2x + 5) = 0 Reorder the terms: 5(-7 + 6x)(5 + 2x) = 0 Multiply (-7 + 6x) * (5 + 2x) 5(-7(5 + 2x) + 6x * (5 + 2x)) = 0 5((5 * -7 + 2x * -7) + 6x * (5 + 2x)) = 0 5((-35 + -14x) + 6x * (5 + 2x)) = 0 5(-35 + -14x + (5 * 6x + 2x * 6x)) = 0 5(-35 + -14x + (30x + 12x2)) = 0 Combine like terms: -14x + 30x = 16x 5(-35 + 16x + 12x2) = 0 (-35 * 5 + 16x * 5 + 12x2 * 5) = 0 (-175 + 80x + 60x2) = 0 Solving -175 + 80x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-35 + 16x + 12x2) = 0 Factor a trinomial. 5((-5 + -2x)(7 + -6x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve: Simplifying 7 + -6x = 0 Solving 7 + -6x = 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 + -6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x = 0 + -7 -6x = 0 + -7 Combine like terms: 0 + -7 = -7 -6x = -7 Divide each side by '-6'. x = 1.166666667 Simplifying x = 1.166666667Solution
x = {-2.5, 1.166666667}
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