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Simplifying (-13y + -12)(9y + 8) + -1(3y + 4)(-13y + -12) = 0 Reorder the terms: (-12 + -13y)(9y + 8) + -1(3y + 4)(-13y + -12) = 0 Reorder the terms: (-12 + -13y)(8 + 9y) + -1(3y + 4)(-13y + -12) = 0 Multiply (-12 + -13y) * (8 + 9y) (-12(8 + 9y) + -13y * (8 + 9y)) + -1(3y + 4)(-13y + -12) = 0 ((8 * -12 + 9y * -12) + -13y * (8 + 9y)) + -1(3y + 4)(-13y + -12) = 0 ((-96 + -108y) + -13y * (8 + 9y)) + -1(3y + 4)(-13y + -12) = 0 (-96 + -108y + (8 * -13y + 9y * -13y)) + -1(3y + 4)(-13y + -12) = 0 (-96 + -108y + (-104y + -117y2)) + -1(3y + 4)(-13y + -12) = 0 Combine like terms: -108y + -104y = -212y (-96 + -212y + -117y2) + -1(3y + 4)(-13y + -12) = 0 Reorder the terms: -96 + -212y + -117y2 + -1(4 + 3y)(-13y + -12) = 0 Reorder the terms: -96 + -212y + -117y2 + -1(4 + 3y)(-12 + -13y) = 0 Multiply (4 + 3y) * (-12 + -13y) -96 + -212y + -117y2 + -1(4(-12 + -13y) + 3y * (-12 + -13y)) = 0 -96 + -212y + -117y2 + -1((-12 * 4 + -13y * 4) + 3y * (-12 + -13y)) = 0 -96 + -212y + -117y2 + -1((-48 + -52y) + 3y * (-12 + -13y)) = 0 -96 + -212y + -117y2 + -1(-48 + -52y + (-12 * 3y + -13y * 3y)) = 0 -96 + -212y + -117y2 + -1(-48 + -52y + (-36y + -39y2)) = 0 Combine like terms: -52y + -36y = -88y -96 + -212y + -117y2 + -1(-48 + -88y + -39y2) = 0 -96 + -212y + -117y2 + (-48 * -1 + -88y * -1 + -39y2 * -1) = 0 -96 + -212y + -117y2 + (48 + 88y + 39y2) = 0 Reorder the terms: -96 + 48 + -212y + 88y + -117y2 + 39y2 = 0 Combine like terms: -96 + 48 = -48 -48 + -212y + 88y + -117y2 + 39y2 = 0 Combine like terms: -212y + 88y = -124y -48 + -124y + -117y2 + 39y2 = 0 Combine like terms: -117y2 + 39y2 = -78y2 -48 + -124y + -78y2 = 0 Solving -48 + -124y + -78y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-2'. -2(24 + 62y + 39y2) = 0 Factor a trinomial. -2((12 + 13y)(2 + 3y)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(12 + 13y)' equal to zero and attempt to solve: Simplifying 12 + 13y = 0 Solving 12 + 13y = 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 + 13y = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 13y = 0 + -12 13y = 0 + -12 Combine like terms: 0 + -12 = -12 13y = -12 Divide each side by '13'. y = -0.9230769231 Simplifying y = -0.9230769231Subproblem 2
Set the factor '(2 + 3y)' equal to zero and attempt to solve: Simplifying 2 + 3y = 0 Solving 2 + 3y = 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 + 3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3y = 0 + -2 3y = 0 + -2 Combine like terms: 0 + -2 = -2 3y = -2 Divide each side by '3'. y = -0.6666666667 Simplifying y = -0.6666666667Solution
y = {-0.9230769231, -0.6666666667}
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