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Simplifying z(5z + -6)(z + 2) = 0 Reorder the terms: z(-6 + 5z)(z + 2) = 0 Reorder the terms: z(-6 + 5z)(2 + z) = 0 Multiply (-6 + 5z) * (2 + z) z(-6(2 + z) + 5z * (2 + z)) = 0 z((2 * -6 + z * -6) + 5z * (2 + z)) = 0 z((-12 + -6z) + 5z * (2 + z)) = 0 z(-12 + -6z + (2 * 5z + z * 5z)) = 0 z(-12 + -6z + (10z + 5z2)) = 0 Combine like terms: -6z + 10z = 4z z(-12 + 4z + 5z2) = 0 (-12 * z + 4z * z + 5z2 * z) = 0 (-12z + 4z2 + 5z3) = 0 Solving -12z + 4z2 + 5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-12 + 4z + 5z2) = 0 Factor a trinomial. z((-2 + -1z)(6 + -5z)) = 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 '(-2 + -1z)' equal to zero and attempt to solve: Simplifying -2 + -1z = 0 Solving -2 + -1z = 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 + -1z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1z = 0 + 2 -1z = 0 + 2 Combine like terms: 0 + 2 = 2 -1z = 2 Divide each side by '-1'. z = -2 Simplifying z = -2Subproblem 3
Set the factor '(6 + -5z)' equal to zero and attempt to solve: Simplifying 6 + -5z = 0 Solving 6 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5z = 0 + -6 -5z = 0 + -6 Combine like terms: 0 + -6 = -6 -5z = -6 Divide each side by '-5'. z = 1.2 Simplifying z = 1.2Solution
z = {0, -2, 1.2}
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