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Simplifying z(3z + -6) = (z + -6)(z + -6) Reorder the terms: z(-6 + 3z) = (z + -6)(z + -6) (-6 * z + 3z * z) = (z + -6)(z + -6) (-6z + 3z2) = (z + -6)(z + -6) Reorder the terms: -6z + 3z2 = (-6 + z)(z + -6) Reorder the terms: -6z + 3z2 = (-6 + z)(-6 + z) Multiply (-6 + z) * (-6 + z) -6z + 3z2 = (-6(-6 + z) + z(-6 + z)) -6z + 3z2 = ((-6 * -6 + z * -6) + z(-6 + z)) -6z + 3z2 = ((36 + -6z) + z(-6 + z)) -6z + 3z2 = (36 + -6z + (-6 * z + z * z)) -6z + 3z2 = (36 + -6z + (-6z + z2)) Combine like terms: -6z + -6z = -12z -6z + 3z2 = (36 + -12z + z2) Solving -6z + 3z2 = 36 + -12z + z2 Solving for variable 'z'. Reorder the terms: -36 + -6z + 12z + 3z2 + -1z2 = 36 + -12z + z2 + -36 + 12z + -1z2 Combine like terms: -6z + 12z = 6z -36 + 6z + 3z2 + -1z2 = 36 + -12z + z2 + -36 + 12z + -1z2 Combine like terms: 3z2 + -1z2 = 2z2 -36 + 6z + 2z2 = 36 + -12z + z2 + -36 + 12z + -1z2 Reorder the terms: -36 + 6z + 2z2 = 36 + -36 + -12z + 12z + z2 + -1z2 Combine like terms: 36 + -36 = 0 -36 + 6z + 2z2 = 0 + -12z + 12z + z2 + -1z2 -36 + 6z + 2z2 = -12z + 12z + z2 + -1z2 Combine like terms: -12z + 12z = 0 -36 + 6z + 2z2 = 0 + z2 + -1z2 -36 + 6z + 2z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 -36 + 6z + 2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 3z + z2) = 0 Factor a trinomial. 2((-6 + -1z)(3 + -1z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve: Simplifying -6 + -1z = 0 Solving -6 + -1z = 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 + -1z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1z = 0 + 6 -1z = 0 + 6 Combine like terms: 0 + 6 = 6 -1z = 6 Divide each side by '-1'. z = -6 Simplifying z = -6Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {-6, 3}
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