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Simplifying (y + 4)(y + -3) + (y + -2)(y + -3) = 0 Reorder the terms: (4 + y)(y + -3) + (y + -2)(y + -3) = 0 Reorder the terms: (4 + y)(-3 + y) + (y + -2)(y + -3) = 0 Multiply (4 + y) * (-3 + y) (4(-3 + y) + y(-3 + y)) + (y + -2)(y + -3) = 0 ((-3 * 4 + y * 4) + y(-3 + y)) + (y + -2)(y + -3) = 0 ((-12 + 4y) + y(-3 + y)) + (y + -2)(y + -3) = 0 (-12 + 4y + (-3 * y + y * y)) + (y + -2)(y + -3) = 0 (-12 + 4y + (-3y + y2)) + (y + -2)(y + -3) = 0 Combine like terms: 4y + -3y = 1y (-12 + 1y + y2) + (y + -2)(y + -3) = 0 Reorder the terms: -12 + 1y + y2 + (-2 + y)(y + -3) = 0 Reorder the terms: -12 + 1y + y2 + (-2 + y)(-3 + y) = 0 Multiply (-2 + y) * (-3 + y) -12 + 1y + y2 + (-2(-3 + y) + y(-3 + y)) = 0 -12 + 1y + y2 + ((-3 * -2 + y * -2) + y(-3 + y)) = 0 -12 + 1y + y2 + ((6 + -2y) + y(-3 + y)) = 0 -12 + 1y + y2 + (6 + -2y + (-3 * y + y * y)) = 0 -12 + 1y + y2 + (6 + -2y + (-3y + y2)) = 0 Combine like terms: -2y + -3y = -5y -12 + 1y + y2 + (6 + -5y + y2) = 0 Reorder the terms: -12 + 6 + 1y + -5y + y2 + y2 = 0 Combine like terms: -12 + 6 = -6 -6 + 1y + -5y + y2 + y2 = 0 Combine like terms: 1y + -5y = -4y -6 + -4y + y2 + y2 = 0 Combine like terms: y2 + y2 = 2y2 -6 + -4y + 2y2 = 0 Solving -6 + -4y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -2y + y2) = 0 Factor a trinomial. 2((-1 + -1y)(3 + -1y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1y)' equal to zero and attempt to solve: Simplifying -1 + -1y = 0 Solving -1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1y = 0 + 1 -1y = 0 + 1 Combine like terms: 0 + 1 = 1 -1y = 1 Divide each side by '-1'. y = -1 Simplifying y = -1Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3Solution
y = {-1, 3}
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