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Simplifying -5x3 + 20xz2 = 0 Reorder the terms: 20xz2 + -5x3 = 0 Solving 20xz2 + -5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(4z2 + -1x2) = 0 Factor a difference between two squares. 5x((2z + x)(2z + -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 '(2z + x)' equal to zero and attempt to solve: Simplifying 2z + x = 0 Reorder the terms: x + 2z = 0 Solving x + 2z = 0 Move all terms containing x to the left, all other terms to the right. Add '-2z' to each side of the equation. x + 2z + -2z = 0 + -2z Combine like terms: 2z + -2z = 0 x + 0 = 0 + -2z x = 0 + -2z Remove the zero: x = -2z Simplifying x = -2zSubproblem 3
Set the factor '(2z + -1x)' equal to zero and attempt to solve: Simplifying 2z + -1x = 0 Reorder the terms: -1x + 2z = 0 Solving -1x + 2z = 0 Move all terms containing x to the left, all other terms to the right. Add '-2z' to each side of the equation. -1x + 2z + -2z = 0 + -2z Combine like terms: 2z + -2z = 0 -1x + 0 = 0 + -2z -1x = 0 + -2z Remove the zero: -1x = -2z Divide each side by '-1'. x = 2z Simplifying x = 2zSolution
x = {0, -2z, 2z}
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