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Simplifying -7(y2 + 18y + 81) = -1372 Reorder the terms: -7(81 + 18y + y2) = -1372 (81 * -7 + 18y * -7 + y2 * -7) = -1372 (-567 + -126y + -7y2) = -1372 Solving -567 + -126y + -7y2 = -1372 Solving for variable 'y'. Reorder the terms: -567 + 1372 + -126y + -7y2 = -1372 + 1372 Combine like terms: -567 + 1372 = 805 805 + -126y + -7y2 = -1372 + 1372 Combine like terms: -1372 + 1372 = 0 805 + -126y + -7y2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(115 + -18y + -1y2) = 0 Factor a trinomial. 7((5 + -1y)(23 + y)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve: Simplifying 5 + -1y = 0 Solving 5 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y = 0 + -5 -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -1y = -5 Divide each side by '-1'. y = 5 Simplifying y = 5Subproblem 2
Set the factor '(23 + y)' equal to zero and attempt to solve: Simplifying 23 + y = 0 Solving 23 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + y = 0 + -23 Combine like terms: 23 + -23 = 0 0 + y = 0 + -23 y = 0 + -23 Combine like terms: 0 + -23 = -23 y = -23 Simplifying y = -23Solution
y = {5, -23}
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