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Simplifying 5x(x + -2)(x + 3) = 0 Reorder the terms: 5x(-2 + x)(x + 3) = 0 Reorder the terms: 5x(-2 + x)(3 + x) = 0 Multiply (-2 + x) * (3 + x) 5x(-2(3 + x) + x(3 + x)) = 0 5x((3 * -2 + x * -2) + x(3 + x)) = 0 5x((-6 + -2x) + x(3 + x)) = 0 5x(-6 + -2x + (3 * x + x * x)) = 0 5x(-6 + -2x + (3x + x2)) = 0 Combine like terms: -2x + 3x = 1x 5x(-6 + 1x + x2) = 0 (-6 * 5x + 1x * 5x + x2 * 5x) = 0 (-30x + 5x2 + 5x3) = 0 Solving -30x + 5x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(-6 + x + x2) = 0 Factor a trinomial. 5x((-3 + -1x)(2 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = -3Subproblem 3
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 = 2Solution
x = {0, -3, 2}
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