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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((-4 + -1z)(2 + -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 '(-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.Subproblem 3
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.Solution
x = {0}
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