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Simplifying y2 + 6y + -14 = 4y + 1 Reorder the terms: -14 + 6y + y2 = 4y + 1 Reorder the terms: -14 + 6y + y2 = 1 + 4y Solving -14 + 6y + y2 = 1 + 4y Solving for variable 'y'. Reorder the terms: -14 + -1 + 6y + -4y + y2 = 1 + 4y + -1 + -4y Combine like terms: -14 + -1 = -15 -15 + 6y + -4y + y2 = 1 + 4y + -1 + -4y Combine like terms: 6y + -4y = 2y -15 + 2y + y2 = 1 + 4y + -1 + -4y Reorder the terms: -15 + 2y + y2 = 1 + -1 + 4y + -4y Combine like terms: 1 + -1 = 0 -15 + 2y + y2 = 0 + 4y + -4y -15 + 2y + y2 = 4y + -4y Combine like terms: 4y + -4y = 0 -15 + 2y + y2 = 0 Factor a trinomial. (-5 + -1y)(3 + -1y) = 0Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve: Simplifying -5 + -1y = 0 Solving -5 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1y = 0 + 5 -1y = 0 + 5 Combine like terms: 0 + 5 = 5 -1y = 5 Divide each side by '-1'. y = -5 Simplifying y = -5Subproblem 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 = {-5, 3}
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