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Simplifying 12xz2 + 36x2z + -120x3 = 0 Solving 12xz2 + 36x2z + -120x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12x'. 12x(z2 + 3xz + -10x2) = 0 Factor a trinomial. 12x((z + -2x)(z + 5x)) = 0 Ignore the factor 12.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 '(z + -2x)' equal to zero and attempt to solve: Simplifying z + -2x = 0 Reorder the terms: -2x + z = 0 Solving -2x + z = 0 Move all terms containing x to the left, all other terms to the right. Add '-1z' to each side of the equation. -2x + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 -2x + 0 = 0 + -1z -2x = 0 + -1z Remove the zero: -2x = -1z Divide each side by '-2'. x = 0.5z Simplifying x = 0.5zSubproblem 3
Set the factor '(z + 5x)' equal to zero and attempt to solve: Simplifying z + 5x = 0 Reorder the terms: 5x + z = 0 Solving 5x + z = 0 Move all terms containing x to the left, all other terms to the right. Add '-1z' to each side of the equation. 5x + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 5x + 0 = 0 + -1z 5x = 0 + -1z Remove the zero: 5x = -1z Divide each side by '5'. x = -0.2z Simplifying x = -0.2zSolution
x = {0, 0.5z, -0.2z}
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