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Simplifying 5(x + -6)(3x + 7) = 0 Reorder the terms: 5(-6 + x)(3x + 7) = 0 Reorder the terms: 5(-6 + x)(7 + 3x) = 0 Multiply (-6 + x) * (7 + 3x) 5(-6(7 + 3x) + x(7 + 3x)) = 0 5((7 * -6 + 3x * -6) + x(7 + 3x)) = 0 5((-42 + -18x) + x(7 + 3x)) = 0 5(-42 + -18x + (7 * x + 3x * x)) = 0 5(-42 + -18x + (7x + 3x2)) = 0 Combine like terms: -18x + 7x = -11x 5(-42 + -11x + 3x2) = 0 (-42 * 5 + -11x * 5 + 3x2 * 5) = 0 (-210 + -55x + 15x2) = 0 Solving -210 + -55x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-42 + -11x + 3x2) = 0 Factor a trinomial. 5((-7 + -3x)(6 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve: Simplifying -7 + -3x = 0 Solving -7 + -3x = 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 + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x = 0 + 7 -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -3x = 7 Divide each side by '-3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-2.333333333, 6}
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