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Simplifying 5(2x + -3)(x + 6) = 0 Reorder the terms: 5(-3 + 2x)(x + 6) = 0 Reorder the terms: 5(-3 + 2x)(6 + x) = 0 Multiply (-3 + 2x) * (6 + x) 5(-3(6 + x) + 2x * (6 + x)) = 0 5((6 * -3 + x * -3) + 2x * (6 + x)) = 0 5((-18 + -3x) + 2x * (6 + x)) = 0 5(-18 + -3x + (6 * 2x + x * 2x)) = 0 5(-18 + -3x + (12x + 2x2)) = 0 Combine like terms: -3x + 12x = 9x 5(-18 + 9x + 2x2) = 0 (-18 * 5 + 9x * 5 + 2x2 * 5) = 0 (-90 + 45x + 10x2) = 0 Solving -90 + 45x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-18 + 9x + 2x2) = 0 Factor a trinomial. 5((-6 + -1x)(3 + -2x)) = 0 Ignore the factor 5.Subproblem 1
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 = -6Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-6, 1.5}
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