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Simplifying 2z2 = 13z + 15 Reorder the terms: 2z2 = 15 + 13z Solving 2z2 = 15 + 13z Solving for variable 'z'. Reorder the terms: -15 + -13z + 2z2 = 15 + 13z + -15 + -13z Reorder the terms: -15 + -13z + 2z2 = 15 + -15 + 13z + -13z Combine like terms: 15 + -15 = 0 -15 + -13z + 2z2 = 0 + 13z + -13z -15 + -13z + 2z2 = 13z + -13z Combine like terms: 13z + -13z = 0 -15 + -13z + 2z2 = 0 Factor a trinomial. (-1 + -1z)(15 + -2z) = 0Subproblem 1
Set the factor '(-1 + -1z)' equal to zero and attempt to solve: Simplifying -1 + -1z = 0 Solving -1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1z = 0 + 1 -1z = 0 + 1 Combine like terms: 0 + 1 = 1 -1z = 1 Divide each side by '-1'. z = -1 Simplifying z = -1Subproblem 2
Set the factor '(15 + -2z)' equal to zero and attempt to solve: Simplifying 15 + -2z = 0 Solving 15 + -2z = 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 + -2z = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2z = 0 + -15 -2z = 0 + -15 Combine like terms: 0 + -15 = -15 -2z = -15 Divide each side by '-2'. z = 7.5 Simplifying z = 7.5Solution
z = {-1, 7.5}
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