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Simplifying y2 + 3y + -29 = 4y + 1 Reorder the terms: -29 + 3y + y2 = 4y + 1 Reorder the terms: -29 + 3y + y2 = 1 + 4y Solving -29 + 3y + y2 = 1 + 4y Solving for variable 'y'. Reorder the terms: -29 + -1 + 3y + -4y + y2 = 1 + 4y + -1 + -4y Combine like terms: -29 + -1 = -30 -30 + 3y + -4y + y2 = 1 + 4y + -1 + -4y Combine like terms: 3y + -4y = -1y -30 + -1y + y2 = 1 + 4y + -1 + -4y Reorder the terms: -30 + -1y + y2 = 1 + -1 + 4y + -4y Combine like terms: 1 + -1 = 0 -30 + -1y + y2 = 0 + 4y + -4y -30 + -1y + y2 = 4y + -4y Combine like terms: 4y + -4y = 0 -30 + -1y + y2 = 0 Factor a trinomial. (-5 + -1y)(6 + -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 '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6Solution
y = {-5, 6}
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