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Simplifying (3z + 1) * x(z + -2) = 0 Reorder the terms: (1 + 3z) * x(z + -2) = 0 Reorder the terms: (1 + 3z) * x(-2 + z) = 0 Reorder the terms for easier multiplication: x(1 + 3z)(-2 + z) = 0 Multiply (1 + 3z) * (-2 + z) x(1(-2 + z) + 3z * (-2 + z)) = 0 x((-2 * 1 + z * 1) + 3z * (-2 + z)) = 0 x((-2 + 1z) + 3z * (-2 + z)) = 0 x(-2 + 1z + (-2 * 3z + z * 3z)) = 0 x(-2 + 1z + (-6z + 3z2)) = 0 Combine like terms: 1z + -6z = -5z x(-2 + -5z + 3z2) = 0 (-2 * x + -5z * x + 3z2 * x) = 0 (-2x + -5xz + 3xz2) = 0 Solving -2x + -5xz + 3xz2 = 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(-2 + -5z + 3z2) = 0 Factor a trinomial. x((-1 + -3z)(2 + -1z)) = 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 '(-1 + -3z)' equal to zero and attempt to solve: Simplifying -1 + -3z = 0 Solving -1 + -3z = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3z = 0 + 1 -3z = 0 + 1 Combine like terms: 0 + 1 = 1 -3z = 1 Add '3z' to each side of the equation. -3z + 3z = 1 + 3z Combine like terms: -3z + 3z = 0 0 = 1 + 3z Simplifying 0 = 1 + 3z 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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