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Simplifying (z + 2) * x(z + 4) = 0 Reorder the terms: (2 + z) * x(z + 4) = 0 Reorder the terms: (2 + z) * x(4 + z) = 0 Reorder the terms for easier multiplication: x(2 + z)(4 + z) = 0 Multiply (2 + z) * (4 + z) x(2(4 + z) + z(4 + z)) = 0 x((4 * 2 + z * 2) + z(4 + z)) = 0 x((8 + 2z) + z(4 + z)) = 0 x(8 + 2z + (4 * z + z * z)) = 0 x(8 + 2z + (4z + z2)) = 0 Combine like terms: 2z + 4z = 6z x(8 + 6z + z2) = 0 (8 * x + 6z * x + z2 * x) = 0 (8x + 6xz + xz2) = 0 Solving 8x + 6xz + xz2 = 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), 'x'. x(8 + 6z + z2) = 0 Factor a trinomial. x((4 + z)(2 + z)) = 0Subproblem 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 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 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 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 z = -4 Add '-1z' to each side of the equation. z + -1z = -4 + -1z Combine like terms: z + -1z = 0 0 = -4 + -1z Simplifying 0 = -4 + -1z 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 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 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 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Add '-1z' to each side of the equation. z + -1z = -2 + -1z Combine like terms: z + -1z = 0 0 = -2 + -1z Simplifying 0 = -2 + -1z 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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