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Simplifying (y + -3)(y + -7) = 12 Reorder the terms: (-3 + y)(y + -7) = 12 Reorder the terms: (-3 + y)(-7 + y) = 12 Multiply (-3 + y) * (-7 + y) (-3(-7 + y) + y(-7 + y)) = 12 ((-7 * -3 + y * -3) + y(-7 + y)) = 12 ((21 + -3y) + y(-7 + y)) = 12 (21 + -3y + (-7 * y + y * y)) = 12 (21 + -3y + (-7y + y2)) = 12 Combine like terms: -3y + -7y = -10y (21 + -10y + y2) = 12 Solving 21 + -10y + y2 = 12 Solving for variable 'y'. Reorder the terms: 21 + -12 + -10y + y2 = 12 + -12 Combine like terms: 21 + -12 = 9 9 + -10y + y2 = 12 + -12 Combine like terms: 12 + -12 = 0 9 + -10y + y2 = 0 Factor a trinomial. (1 + -1y)(9 + -1y) = 0Subproblem 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 '(9 + -1y)' equal to zero and attempt to solve: Simplifying 9 + -1y = 0 Solving 9 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1y = 0 + -9 -1y = 0 + -9 Combine like terms: 0 + -9 = -9 -1y = -9 Divide each side by '-1'. y = 9 Simplifying y = 9Solution
y = {1, 9}
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