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Simplifying (10x2 + 20x) * x(x3 + -2x2) = 0 Reorder the terms: (20x + 10x2) * x(x3 + -2x2) = 0 Reorder the terms: (20x + 10x2) * x(-2x2 + x3) = 0 Reorder the terms for easier multiplication: x(20x + 10x2)(-2x2 + x3) = 0 Multiply (20x + 10x2) * (-2x2 + x3) x(20x * (-2x2 + x3) + 10x2 * (-2x2 + x3)) = 0 x((-2x2 * 20x + x3 * 20x) + 10x2 * (-2x2 + x3)) = 0 x((-40x3 + 20x4) + 10x2 * (-2x2 + x3)) = 0 x(-40x3 + 20x4 + (-2x2 * 10x2 + x3 * 10x2)) = 0 x(-40x3 + 20x4 + (-20x4 + 10x5)) = 0 Combine like terms: 20x4 + -20x4 = 0 x(-40x3 + 0 + 10x5) = 0 x(-40x3 + 10x5) = 0 (-40x3 * x + 10x5 * x) = 0 (-40x4 + 10x6) = 0 Solving -40x4 + 10x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x4'. 10x4(-4 + x2) = 0 Factor a difference between two squares. 10x4((2 + x)(-2 + x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {-2, 2}
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