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Simplifying (3z + -8)(4 + z) = 0 Reorder the terms: (-8 + 3z)(4 + z) = 0 Multiply (-8 + 3z) * (4 + z) (-8(4 + z) + 3z * (4 + z)) = 0 ((4 * -8 + z * -8) + 3z * (4 + z)) = 0 ((-32 + -8z) + 3z * (4 + z)) = 0 (-32 + -8z + (4 * 3z + z * 3z)) = 0 (-32 + -8z + (12z + 3z2)) = 0 Combine like terms: -8z + 12z = 4z (-32 + 4z + 3z2) = 0 Solving -32 + 4z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-4 + -1z)(8 + -3z) = 0Subproblem 1
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 = -4Subproblem 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 = {-4, 2.666666667}
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