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