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Simplifying (2z + 9)(z + -7) = 0 Reorder the terms: (9 + 2z)(z + -7) = 0 Reorder the terms: (9 + 2z)(-7 + z) = 0 Multiply (9 + 2z) * (-7 + z) (9(-7 + z) + 2z * (-7 + z)) = 0 ((-7 * 9 + z * 9) + 2z * (-7 + z)) = 0 ((-63 + 9z) + 2z * (-7 + z)) = 0 (-63 + 9z + (-7 * 2z + z * 2z)) = 0 (-63 + 9z + (-14z + 2z2)) = 0 Combine like terms: 9z + -14z = -5z (-63 + -5z + 2z2) = 0 Solving -63 + -5z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -2z)(7 + -1z) = 0Subproblem 1
Set the factor '(-9 + -2z)' equal to zero and attempt to solve: Simplifying -9 + -2z = 0 Solving -9 + -2z = 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 + -2z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2z = 0 + 9 -2z = 0 + 9 Combine like terms: 0 + 9 = 9 -2z = 9 Divide each side by '-2'. z = -4.5 Simplifying z = -4.5Subproblem 2
Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7Solution
z = {-4.5, 7}
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