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Simplifying (y + -2)(y + -7) = 6 Reorder the terms: (-2 + y)(y + -7) = 6 Reorder the terms: (-2 + y)(-7 + y) = 6 Multiply (-2 + y) * (-7 + y) (-2(-7 + y) + y(-7 + y)) = 6 ((-7 * -2 + y * -2) + y(-7 + y)) = 6 ((14 + -2y) + y(-7 + y)) = 6 (14 + -2y + (-7 * y + y * y)) = 6 (14 + -2y + (-7y + y2)) = 6 Combine like terms: -2y + -7y = -9y (14 + -9y + y2) = 6 Solving 14 + -9y + y2 = 6 Solving for variable 'y'. Reorder the terms: 14 + -6 + -9y + y2 = 6 + -6 Combine like terms: 14 + -6 = 8 8 + -9y + y2 = 6 + -6 Combine like terms: 6 + -6 = 0 8 + -9y + y2 = 0 Factor a trinomial. (1 + -1y)(8 + -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 '(8 + -1y)' equal to zero and attempt to solve: Simplifying 8 + -1y = 0 Solving 8 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1y = 0 + -8 -1y = 0 + -8 Combine like terms: 0 + -8 = -8 -1y = -8 Divide each side by '-1'. y = 8 Simplifying y = 8Solution
y = {1, 8}
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