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Simplifying (y + -5)(y + -4) = 3y Reorder the terms: (-5 + y)(y + -4) = 3y Reorder the terms: (-5 + y)(-4 + y) = 3y Multiply (-5 + y) * (-4 + y) (-5(-4 + y) + y(-4 + y)) = 3y ((-4 * -5 + y * -5) + y(-4 + y)) = 3y ((20 + -5y) + y(-4 + y)) = 3y (20 + -5y + (-4 * y + y * y)) = 3y (20 + -5y + (-4y + y2)) = 3y Combine like terms: -5y + -4y = -9y (20 + -9y + y2) = 3y Solving 20 + -9y + y2 = 3y Solving for variable 'y'. Reorder the terms: 20 + -9y + -3y + y2 = 3y + -3y Combine like terms: -9y + -3y = -12y 20 + -12y + y2 = 3y + -3y Combine like terms: 3y + -3y = 0 20 + -12y + y2 = 0 Factor a trinomial. (2 + -1y)(10 + -1y) = 0Subproblem 1
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 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 = {2, 10}
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