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Simplifying 3(z + -6) = (z + -6)(z + -6) Reorder the terms: 3(-6 + z) = (z + -6)(z + -6) (-6 * 3 + z * 3) = (z + -6)(z + -6) (-18 + 3z) = (z + -6)(z + -6) Reorder the terms: -18 + 3z = (-6 + z)(z + -6) Reorder the terms: -18 + 3z = (-6 + z)(-6 + z) Multiply (-6 + z) * (-6 + z) -18 + 3z = (-6(-6 + z) + z(-6 + z)) -18 + 3z = ((-6 * -6 + z * -6) + z(-6 + z)) -18 + 3z = ((36 + -6z) + z(-6 + z)) -18 + 3z = (36 + -6z + (-6 * z + z * z)) -18 + 3z = (36 + -6z + (-6z + z2)) Combine like terms: -6z + -6z = -12z -18 + 3z = (36 + -12z + z2) Solving -18 + 3z = 36 + -12z + z2 Solving for variable 'z'. Reorder the terms: -18 + -36 + 3z + 12z + -1z2 = 36 + -12z + z2 + -36 + 12z + -1z2 Combine like terms: -18 + -36 = -54 -54 + 3z + 12z + -1z2 = 36 + -12z + z2 + -36 + 12z + -1z2 Combine like terms: 3z + 12z = 15z -54 + 15z + -1z2 = 36 + -12z + z2 + -36 + 12z + -1z2 Reorder the terms: -54 + 15z + -1z2 = 36 + -36 + -12z + 12z + z2 + -1z2 Combine like terms: 36 + -36 = 0 -54 + 15z + -1z2 = 0 + -12z + 12z + z2 + -1z2 -54 + 15z + -1z2 = -12z + 12z + z2 + -1z2 Combine like terms: -12z + 12z = 0 -54 + 15z + -1z2 = 0 + z2 + -1z2 -54 + 15z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 -54 + 15z + -1z2 = 0 Factor a trinomial. (-9 + z)(6 + -1z) = 0Subproblem 1
Set the factor '(-9 + z)' equal to zero and attempt to solve: Simplifying -9 + z = 0 Solving -9 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + z = 0 + 9 z = 0 + 9 Combine like terms: 0 + 9 = 9 z = 9 Simplifying z = 9Subproblem 2
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 = 6Solution
z = {9, 6}
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