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Simplifying (z + -5)(z + 4) = 36 Reorder the terms: (-5 + z)(z + 4) = 36 Reorder the terms: (-5 + z)(4 + z) = 36 Multiply (-5 + z) * (4 + z) (-5(4 + z) + z(4 + z)) = 36 ((4 * -5 + z * -5) + z(4 + z)) = 36 ((-20 + -5z) + z(4 + z)) = 36 (-20 + -5z + (4 * z + z * z)) = 36 (-20 + -5z + (4z + z2)) = 36 Combine like terms: -5z + 4z = -1z (-20 + -1z + z2) = 36 Solving -20 + -1z + z2 = 36 Solving for variable 'z'. Reorder the terms: -20 + -36 + -1z + z2 = 36 + -36 Combine like terms: -20 + -36 = -56 -56 + -1z + z2 = 36 + -36 Combine like terms: 36 + -36 = 0 -56 + -1z + z2 = 0 Factor a trinomial. (-7 + -1z)(8 + -1z) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Solution
z = {-7, 8}
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