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Simplifying 2x(2x + 1)(x + -5) = 0 Reorder the terms: 2x(1 + 2x)(x + -5) = 0 Reorder the terms: 2x(1 + 2x)(-5 + x) = 0 Multiply (1 + 2x) * (-5 + x) 2x(1(-5 + x) + 2x * (-5 + x)) = 0 2x((-5 * 1 + x * 1) + 2x * (-5 + x)) = 0 2x((-5 + 1x) + 2x * (-5 + x)) = 0 2x(-5 + 1x + (-5 * 2x + x * 2x)) = 0 2x(-5 + 1x + (-10x + 2x2)) = 0 Combine like terms: 1x + -10x = -9x 2x(-5 + -9x + 2x2) = 0 (-5 * 2x + -9x * 2x + 2x2 * 2x) = 0 (-10x + -18x2 + 4x3) = 0 Solving -10x + -18x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-5 + -9x + 2x2) = 0 Factor a trinomial. 2x((-1 + -2x)(5 + -1x)) = 0 Ignore the factor 2.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 '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, -0.5, 5}
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