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Simplifying 5x(x + -1) = 30 Reorder the terms: 5x(-1 + x) = 30 (-1 * 5x + x * 5x) = 30 (-5x + 5x2) = 30 Solving -5x + 5x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -5x + 5x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -5x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + -1x + x2) = 0 Factor a trinomial. 5((-2 + -1x)(3 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-2, 3}
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