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Simplifying (z + -5)(z + 4) + -70 = 0 Reorder the terms: (-5 + z)(z + 4) + -70 = 0 Reorder the terms: (-5 + z)(4 + z) + -70 = 0 Multiply (-5 + z) * (4 + z) (-5(4 + z) + z(4 + z)) + -70 = 0 ((4 * -5 + z * -5) + z(4 + z)) + -70 = 0 ((-20 + -5z) + z(4 + z)) + -70 = 0 (-20 + -5z + (4 * z + z * z)) + -70 = 0 (-20 + -5z + (4z + z2)) + -70 = 0 Combine like terms: -5z + 4z = -1z (-20 + -1z + z2) + -70 = 0 Reorder the terms: -20 + -70 + -1z + z2 = 0 Combine like terms: -20 + -70 = -90 -90 + -1z + z2 = 0 Solving -90 + -1z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -1z)(10 + -1z) = 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 '(10 + -1z)' equal to zero and attempt to solve: Simplifying 10 + -1z = 0 Solving 10 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1z = 0 + -10 -1z = 0 + -10 Combine like terms: 0 + -10 = -10 -1z = -10 Divide each side by '-1'. z = 10 Simplifying z = 10Solution
z = {-9, 10}
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