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Simplifying (3z + -2)(8 + z) = 0 Reorder the terms: (-2 + 3z)(8 + z) = 0 Multiply (-2 + 3z) * (8 + z) (-2(8 + z) + 3z * (8 + z)) = 0 ((8 * -2 + z * -2) + 3z * (8 + z)) = 0 ((-16 + -2z) + 3z * (8 + z)) = 0 (-16 + -2z + (8 * 3z + z * 3z)) = 0 (-16 + -2z + (24z + 3z2)) = 0 Combine like terms: -2z + 24z = 22z (-16 + 22z + 3z2) = 0 Solving -16 + 22z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + -1z)(2 + -3z) = 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 '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {-8, 0.6666666667}
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