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Simplifying (2z + -8) * x(3z + 6) = 0 Reorder the terms: (-8 + 2z) * x(3z + 6) = 0 Reorder the terms: (-8 + 2z) * x(6 + 3z) = 0 Reorder the terms for easier multiplication: x(-8 + 2z)(6 + 3z) = 0 Multiply (-8 + 2z) * (6 + 3z) x(-8(6 + 3z) + 2z * (6 + 3z)) = 0 x((6 * -8 + 3z * -8) + 2z * (6 + 3z)) = 0 x((-48 + -24z) + 2z * (6 + 3z)) = 0 x(-48 + -24z + (6 * 2z + 3z * 2z)) = 0 x(-48 + -24z + (12z + 6z2)) = 0 Combine like terms: -24z + 12z = -12z x(-48 + -12z + 6z2) = 0 (-48 * x + -12z * x + 6z2 * x) = 0 (-48x + -12xz + 6xz2) = 0 Solving -48x + -12xz + 6xz2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-8 + -2z + z2) = 0 Factor a trinomial. 6x((-2 + -1z)(4 + -1z)) = 0 Ignore the factor 6.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 '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 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 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Add 'z' to each side of the equation. -1z + z = 2 + z Combine like terms: -1z + z = 0 0 = 2 + z Simplifying 0 = 2 + z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Add 'z' to each side of the equation. -1z + z = -4 + z Combine like terms: -1z + z = 0 0 = -4 + z Simplifying 0 = -4 + z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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