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Simplifying z2 + 9z + -9 = (2z + 3)(z + -3) Reorder the terms: -9 + 9z + z2 = (2z + 3)(z + -3) Reorder the terms: -9 + 9z + z2 = (3 + 2z)(z + -3) Reorder the terms: -9 + 9z + z2 = (3 + 2z)(-3 + z) Multiply (3 + 2z) * (-3 + z) -9 + 9z + z2 = (3(-3 + z) + 2z * (-3 + z)) -9 + 9z + z2 = ((-3 * 3 + z * 3) + 2z * (-3 + z)) -9 + 9z + z2 = ((-9 + 3z) + 2z * (-3 + z)) -9 + 9z + z2 = (-9 + 3z + (-3 * 2z + z * 2z)) -9 + 9z + z2 = (-9 + 3z + (-6z + 2z2)) Combine like terms: 3z + -6z = -3z -9 + 9z + z2 = (-9 + -3z + 2z2) Add '9' to each side of the equation. -9 + 9z + 9 + z2 = -9 + -3z + 9 + 2z2 Reorder the terms: -9 + 9 + 9z + z2 = -9 + -3z + 9 + 2z2 Combine like terms: -9 + 9 = 0 0 + 9z + z2 = -9 + -3z + 9 + 2z2 9z + z2 = -9 + -3z + 9 + 2z2 Reorder the terms: 9z + z2 = -9 + 9 + -3z + 2z2 Combine like terms: -9 + 9 = 0 9z + z2 = 0 + -3z + 2z2 9z + z2 = -3z + 2z2 Solving 9z + z2 = -3z + 2z2 Solving for variable 'z'. Reorder the terms: 9z + 3z + z2 + -2z2 = -3z + 2z2 + 3z + -2z2 Combine like terms: 9z + 3z = 12z 12z + z2 + -2z2 = -3z + 2z2 + 3z + -2z2 Combine like terms: z2 + -2z2 = -1z2 12z + -1z2 = -3z + 2z2 + 3z + -2z2 Reorder the terms: 12z + -1z2 = -3z + 3z + 2z2 + -2z2 Combine like terms: -3z + 3z = 0 12z + -1z2 = 0 + 2z2 + -2z2 12z + -1z2 = 2z2 + -2z2 Combine like terms: 2z2 + -2z2 = 0 12z + -1z2 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(12 + -1z) = 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 '(12 + -1z)' equal to zero and attempt to solve: Simplifying 12 + -1z = 0 Solving 12 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1z = 0 + -12 -1z = 0 + -12 Combine like terms: 0 + -12 = -12 -1z = -12 Divide each side by '-1'. z = 12 Simplifying z = 12Solution
z = {0, 12}
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