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Simplifying (4y + 3)(y + 4) = 20y + 15 Reorder the terms: (3 + 4y)(y + 4) = 20y + 15 Reorder the terms: (3 + 4y)(4 + y) = 20y + 15 Multiply (3 + 4y) * (4 + y) (3(4 + y) + 4y * (4 + y)) = 20y + 15 ((4 * 3 + y * 3) + 4y * (4 + y)) = 20y + 15 ((12 + 3y) + 4y * (4 + y)) = 20y + 15 (12 + 3y + (4 * 4y + y * 4y)) = 20y + 15 (12 + 3y + (16y + 4y2)) = 20y + 15 Combine like terms: 3y + 16y = 19y (12 + 19y + 4y2) = 20y + 15 Reorder the terms: 12 + 19y + 4y2 = 15 + 20y Solving 12 + 19y + 4y2 = 15 + 20y Solving for variable 'y'. Reorder the terms: 12 + -15 + 19y + -20y + 4y2 = 15 + 20y + -15 + -20y Combine like terms: 12 + -15 = -3 -3 + 19y + -20y + 4y2 = 15 + 20y + -15 + -20y Combine like terms: 19y + -20y = -1y -3 + -1y + 4y2 = 15 + 20y + -15 + -20y Reorder the terms: -3 + -1y + 4y2 = 15 + -15 + 20y + -20y Combine like terms: 15 + -15 = 0 -3 + -1y + 4y2 = 0 + 20y + -20y -3 + -1y + 4y2 = 20y + -20y Combine like terms: 20y + -20y = 0 -3 + -1y + 4y2 = 0 Factor a trinomial. (-3 + -4y)(1 + -1y) = 0Subproblem 1
Set the factor '(-3 + -4y)' equal to zero and attempt to solve: Simplifying -3 + -4y = 0 Solving -3 + -4y = 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 + -4y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4y = 0 + 3 -4y = 0 + 3 Combine like terms: 0 + 3 = 3 -4y = 3 Divide each side by '-4'. y = -0.75 Simplifying y = -0.75Subproblem 2
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 = 1Solution
y = {-0.75, 1}
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