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Simplifying (3z + -8)(3 + z) = 0 Reorder the terms: (-8 + 3z)(3 + z) = 0 Multiply (-8 + 3z) * (3 + z) (-8(3 + z) + 3z * (3 + z)) = 0 ((3 * -8 + z * -8) + 3z * (3 + z)) = 0 ((-24 + -8z) + 3z * (3 + z)) = 0 (-24 + -8z + (3 * 3z + z * 3z)) = 0 (-24 + -8z + (9z + 3z2)) = 0 Combine like terms: -8z + 9z = 1z (-24 + 1z + 3z2) = 0 Solving -24 + 1z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-3 + -1z)(8 + -3z) = 0Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve: Simplifying -3 + -1z = 0 Solving -3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z = 0 + 3 -1z = 0 + 3 Combine like terms: 0 + 3 = 3 -1z = 3 Divide each side by '-1'. z = -3 Simplifying z = -3Subproblem 2
Set the factor '(8 + -3z)' equal to zero and attempt to solve: Simplifying 8 + -3z = 0 Solving 8 + -3z = 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 + -3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3z = 0 + -8 -3z = 0 + -8 Combine like terms: 0 + -8 = -8 -3z = -8 Divide each side by '-3'. z = 2.666666667 Simplifying z = 2.666666667Solution
z = {-3, 2.666666667}
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