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Simplifying z(2z + 1)(3z + -2) = 0 Reorder the terms: z(1 + 2z)(3z + -2) = 0 Reorder the terms: z(1 + 2z)(-2 + 3z) = 0 Multiply (1 + 2z) * (-2 + 3z) z(1(-2 + 3z) + 2z * (-2 + 3z)) = 0 z((-2 * 1 + 3z * 1) + 2z * (-2 + 3z)) = 0 z((-2 + 3z) + 2z * (-2 + 3z)) = 0 z(-2 + 3z + (-2 * 2z + 3z * 2z)) = 0 z(-2 + 3z + (-4z + 6z2)) = 0 Combine like terms: 3z + -4z = -1z z(-2 + -1z + 6z2) = 0 (-2 * z + -1z * z + 6z2 * z) = 0 (-2z + -1z2 + 6z3) = 0 Solving -2z + -1z2 + 6z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-2 + -1z + 6z2) = 0 Factor a trinomial. z((-1 + -2z)(2 + -3z)) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5Subproblem 3
Set the factor '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {0, -0.5, 0.6666666667}
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