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Simplifying (4 + -1z)(5z + 8) = 0 Reorder the terms: (4 + -1z)(8 + 5z) = 0 Multiply (4 + -1z) * (8 + 5z) (4(8 + 5z) + -1z * (8 + 5z)) = 0 ((8 * 4 + 5z * 4) + -1z * (8 + 5z)) = 0 ((32 + 20z) + -1z * (8 + 5z)) = 0 (32 + 20z + (8 * -1z + 5z * -1z)) = 0 (32 + 20z + (-8z + -5z2)) = 0 Combine like terms: 20z + -8z = 12z (32 + 12z + -5z2) = 0 Solving 32 + 12z + -5z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z)(8 + 5z) = 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 + 5z)' equal to zero and attempt to solve: Simplifying 8 + 5z = 0 Solving 8 + 5z = 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 + 5z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5z = 0 + -8 5z = 0 + -8 Combine like terms: 0 + -8 = -8 5z = -8 Divide each side by '5'. z = -1.6 Simplifying z = -1.6Solution
z = {4, -1.6}
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