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Simplifying (7 + -1z)(2z + 5) = 0 Reorder the terms: (7 + -1z)(5 + 2z) = 0 Multiply (7 + -1z) * (5 + 2z) (7(5 + 2z) + -1z * (5 + 2z)) = 0 ((5 * 7 + 2z * 7) + -1z * (5 + 2z)) = 0 ((35 + 14z) + -1z * (5 + 2z)) = 0 (35 + 14z + (5 * -1z + 2z * -1z)) = 0 (35 + 14z + (-5z + -2z2)) = 0 Combine like terms: 14z + -5z = 9z (35 + 9z + -2z2) = 0 Solving 35 + 9z + -2z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -1z)(5 + 2z) = 0Subproblem 1
Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7Subproblem 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 = {7, -2.5}
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