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Simplifying (y + -12)(2y + 14) = 0 Reorder the terms: (-12 + y)(2y + 14) = 0 Reorder the terms: (-12 + y)(14 + 2y) = 0 Multiply (-12 + y) * (14 + 2y) (-12(14 + 2y) + y(14 + 2y)) = 0 ((14 * -12 + 2y * -12) + y(14 + 2y)) = 0 ((-168 + -24y) + y(14 + 2y)) = 0 (-168 + -24y + (14 * y + 2y * y)) = 0 (-168 + -24y + (14y + 2y2)) = 0 Combine like terms: -24y + 14y = -10y (-168 + -10y + 2y2) = 0 Solving -168 + -10y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-84 + -5y + y2) = 0 Factor a trinomial. 2((-7 + -1y)(12 + -1y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve: Simplifying -7 + -1y = 0 Solving -7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1y = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1y = 0 + 7 -1y = 0 + 7 Combine like terms: 0 + 7 = 7 -1y = 7 Divide each side by '-1'. y = -7 Simplifying y = -7Subproblem 2
Set the factor '(12 + -1y)' equal to zero and attempt to solve: Simplifying 12 + -1y = 0 Solving 12 + -1y = 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 + -1y = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1y = 0 + -12 -1y = 0 + -12 Combine like terms: 0 + -12 = -12 -1y = -12 Divide each side by '-1'. y = 12 Simplifying y = 12Solution
y = {-7, 12}
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