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Simplifying (2 + -1z)(2z + 5) = 0 Reorder the terms: (2 + -1z)(5 + 2z) = 0 Multiply (2 + -1z) * (5 + 2z) (2(5 + 2z) + -1z * (5 + 2z)) = 0 ((5 * 2 + 2z * 2) + -1z * (5 + 2z)) = 0 ((10 + 4z) + -1z * (5 + 2z)) = 0 (10 + 4z + (5 * -1z + 2z * -1z)) = 0 (10 + 4z + (-5z + -2z2)) = 0 Combine like terms: 4z + -5z = -1z (10 + -1z + -2z2) = 0 Solving 10 + -1z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -1z)(5 + 2z) = 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 + 2z)' equal to zero and attempt to solve: Simplifying 5 + 2z = 0 Solving 5 + 2z = 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 + 2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2z = 0 + -5 2z = 0 + -5 Combine like terms: 0 + -5 = -5 2z = -5 Divide each side by '2'. z = -2.5 Simplifying z = -2.5Solution
z = {2, -2.5}
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