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Simplifying z2 + 10z = 75 Reorder the terms: 10z + z2 = 75 Solving 10z + z2 = 75 Solving for variable 'z'. Reorder the terms: -75 + 10z + z2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 10z + z2 = 0 Factor a trinomial. (-15 + -1z)(5 + -1z) = 0Subproblem 1
Set the factor '(-15 + -1z)' equal to zero and attempt to solve: Simplifying -15 + -1z = 0 Solving -15 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1z = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1z = 0 + 15 -1z = 0 + 15 Combine like terms: 0 + 15 = 15 -1z = 15 Divide each side by '-1'. z = -15 Simplifying z = -15Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 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 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Solution
z = {-15, 5}
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