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Simplifying (z + 9)(2z + -7) = 0 Reorder the terms: (9 + z)(2z + -7) = 0 Reorder the terms: (9 + z)(-7 + 2z) = 0 Multiply (9 + z) * (-7 + 2z) (9(-7 + 2z) + z(-7 + 2z)) = 0 ((-7 * 9 + 2z * 9) + z(-7 + 2z)) = 0 ((-63 + 18z) + z(-7 + 2z)) = 0 (-63 + 18z + (-7 * z + 2z * z)) = 0 (-63 + 18z + (-7z + 2z2)) = 0 Combine like terms: 18z + -7z = 11z (-63 + 11z + 2z2) = 0 Solving -63 + 11z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -1z)(7 + -2z) = 0Subproblem 1
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 = -9Subproblem 2
Set the factor '(7 + -2z)' equal to zero and attempt to solve: Simplifying 7 + -2z = 0 Solving 7 + -2z = 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 + -2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2z = 0 + -7 -2z = 0 + -7 Combine like terms: 0 + -7 = -7 -2z = -7 Divide each side by '-2'. z = 3.5 Simplifying z = 3.5Solution
z = {-9, 3.5}
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