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Simplifying (5z + -6)(8 + z) = 0 Reorder the terms: (-6 + 5z)(8 + z) = 0 Multiply (-6 + 5z) * (8 + z) (-6(8 + z) + 5z * (8 + z)) = 0 ((8 * -6 + z * -6) + 5z * (8 + z)) = 0 ((-48 + -6z) + 5z * (8 + z)) = 0 (-48 + -6z + (8 * 5z + z * 5z)) = 0 (-48 + -6z + (40z + 5z2)) = 0 Combine like terms: -6z + 40z = 34z (-48 + 34z + 5z2) = 0 Solving -48 + 34z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + -1z)(6 + -5z) = 0Subproblem 1
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 = -8Subproblem 2
Set the factor '(6 + -5z)' equal to zero and attempt to solve: Simplifying 6 + -5z = 0 Solving 6 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5z = 0 + -6 -5z = 0 + -6 Combine like terms: 0 + -6 = -6 -5z = -6 Divide each side by '-5'. z = 1.2 Simplifying z = 1.2Solution
z = {-8, 1.2}
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