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Simplifying 2z2 + 12z + -270 = 0 Reorder the terms: -270 + 12z + 2z2 = 0 Solving -270 + 12z + 2z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-135 + 6z + z2) = 0 Factor a trinomial. 2((-15 + -1z)(9 + -1z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -1z)' equal to zero and attempt to solve: Simplifying -15 + -1z = 0 Solving -15 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1z = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1z = 0 + 15 -1z = 0 + 15 Combine like terms: 0 + 15 = 15 -1z = 15 Divide each side by '-1'. z = -15 Simplifying z = -15Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 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 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Solution
z = {-15, 9}
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