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Simplifying (2 + -1z)(4z + 5) = 0 Reorder the terms: (2 + -1z)(5 + 4z) = 0 Multiply (2 + -1z) * (5 + 4z) (2(5 + 4z) + -1z * (5 + 4z)) = 0 ((5 * 2 + 4z * 2) + -1z * (5 + 4z)) = 0 ((10 + 8z) + -1z * (5 + 4z)) = 0 (10 + 8z + (5 * -1z + 4z * -1z)) = 0 (10 + 8z + (-5z + -4z2)) = 0 Combine like terms: 8z + -5z = 3z (10 + 3z + -4z2) = 0 Solving 10 + 3z + -4z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -1z)(5 + 4z) = 0Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 2
Set the factor '(5 + 4z)' equal to zero and attempt to solve: Simplifying 5 + 4z = 0 Solving 5 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4z = 0 + -5 4z = 0 + -5 Combine like terms: 0 + -5 = -5 4z = -5 Divide each side by '4'. z = -1.25 Simplifying z = -1.25Solution
z = {2, -1.25}
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