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Simplifying (3y + 2)(4y + 1) = 6y + 5 Reorder the terms: (2 + 3y)(4y + 1) = 6y + 5 Reorder the terms: (2 + 3y)(1 + 4y) = 6y + 5 Multiply (2 + 3y) * (1 + 4y) (2(1 + 4y) + 3y * (1 + 4y)) = 6y + 5 ((1 * 2 + 4y * 2) + 3y * (1 + 4y)) = 6y + 5 ((2 + 8y) + 3y * (1 + 4y)) = 6y + 5 (2 + 8y + (1 * 3y + 4y * 3y)) = 6y + 5 (2 + 8y + (3y + 12y2)) = 6y + 5 Combine like terms: 8y + 3y = 11y (2 + 11y + 12y2) = 6y + 5 Reorder the terms: 2 + 11y + 12y2 = 5 + 6y Solving 2 + 11y + 12y2 = 5 + 6y Solving for variable 'y'. Reorder the terms: 2 + -5 + 11y + -6y + 12y2 = 5 + 6y + -5 + -6y Combine like terms: 2 + -5 = -3 -3 + 11y + -6y + 12y2 = 5 + 6y + -5 + -6y Combine like terms: 11y + -6y = 5y -3 + 5y + 12y2 = 5 + 6y + -5 + -6y Reorder the terms: -3 + 5y + 12y2 = 5 + -5 + 6y + -6y Combine like terms: 5 + -5 = 0 -3 + 5y + 12y2 = 0 + 6y + -6y -3 + 5y + 12y2 = 6y + -6y Combine like terms: 6y + -6y = 0 -3 + 5y + 12y2 = 0 Factor a trinomial. (-3 + -4y)(1 + -3y) = 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 + -3y)' equal to zero and attempt to solve: Simplifying 1 + -3y = 0 Solving 1 + -3y = 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 + -3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3y = 0 + -1 -3y = 0 + -1 Combine like terms: 0 + -1 = -1 -3y = -1 Divide each side by '-3'. y = 0.3333333333 Simplifying y = 0.3333333333Solution
y = {-0.75, 0.3333333333}
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