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Simplifying y2(-2 + -1y)(9 + -1y) = 0 Multiply (-2 + -1y) * (9 + -1y) y2(-2(9 + -1y) + -1y * (9 + -1y)) = 0 y2((9 * -2 + -1y * -2) + -1y * (9 + -1y)) = 0 y2((-18 + 2y) + -1y * (9 + -1y)) = 0 y2(-18 + 2y + (9 * -1y + -1y * -1y)) = 0 y2(-18 + 2y + (-9y + 1y2)) = 0 Combine like terms: 2y + -9y = -7y y2(-18 + -7y + 1y2) = 0 (-18 * y2 + -7y * y2 + 1y2 * y2) = 0 (-18y2 + -7y3 + 1y4) = 0 Solving -18y2 + -7y3 + 1y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y2'. y2(-18 + -7y + y2) = 0 Factor a trinomial. y2((-2 + -1y)(9 + -1y)) = 0Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(-2 + -1y)' equal to zero and attempt to solve: Simplifying -2 + -1y = 0 Solving -2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1y = 0 + 2 -1y = 0 + 2 Combine like terms: 0 + 2 = 2 -1y = 2 Divide each side by '-1'. y = -2 Simplifying y = -2Subproblem 3
Set the factor '(9 + -1y)' equal to zero and attempt to solve: Simplifying 9 + -1y = 0 Solving 9 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1y = 0 + -9 -1y = 0 + -9 Combine like terms: 0 + -9 = -9 -1y = -9 Divide each side by '-1'. y = 9 Simplifying y = 9Solution
y = {0, -2, 9}
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