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Simplifying 180y + -360 + -3y2 + 6y = 120y Reorder the terms: -360 + 180y + 6y + -3y2 = 120y Combine like terms: 180y + 6y = 186y -360 + 186y + -3y2 = 120y Solving -360 + 186y + -3y2 = 120y Solving for variable 'y'. Reorder the terms: -360 + 186y + -120y + -3y2 = 120y + -120y Combine like terms: 186y + -120y = 66y -360 + 66y + -3y2 = 120y + -120y Combine like terms: 120y + -120y = 0 -360 + 66y + -3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-120 + 22y + -1y2) = 0 Factor a trinomial. 3((-12 + y)(10 + -1y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + y)' equal to zero and attempt to solve: Simplifying -12 + y = 0 Solving -12 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = 0 + 12 Combine like terms: -12 + 12 = 0 0 + y = 0 + 12 y = 0 + 12 Combine like terms: 0 + 12 = 12 y = 12 Simplifying y = 12Subproblem 2
Set the factor '(10 + -1y)' equal to zero and attempt to solve: Simplifying 10 + -1y = 0 Solving 10 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1y = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1y = 0 + -10 -1y = 0 + -10 Combine like terms: 0 + -10 = -10 -1y = -10 Divide each side by '-1'. y = 10 Simplifying y = 10Solution
y = {12, 10}
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