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Simplifying (3y + -1)(4y + 2) = 0 Reorder the terms: (-1 + 3y)(4y + 2) = 0 Reorder the terms: (-1 + 3y)(2 + 4y) = 0 Multiply (-1 + 3y) * (2 + 4y) (-1(2 + 4y) + 3y * (2 + 4y)) = 0 ((2 * -1 + 4y * -1) + 3y * (2 + 4y)) = 0 ((-2 + -4y) + 3y * (2 + 4y)) = 0 (-2 + -4y + (2 * 3y + 4y * 3y)) = 0 (-2 + -4y + (6y + 12y2)) = 0 Combine like terms: -4y + 6y = 2y (-2 + 2y + 12y2) = 0 Solving -2 + 2y + 12y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + y + 6y2) = 0 Factor a trinomial. 2((-1 + -2y)(1 + -3y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2y)' equal to zero and attempt to solve: Simplifying -1 + -2y = 0 Solving -1 + -2y = 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 + -2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2y = 0 + 1 -2y = 0 + 1 Combine like terms: 0 + 1 = 1 -2y = 1 Divide each side by '-2'. y = -0.5 Simplifying y = -0.5Subproblem 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 = {-0.5, 0.3333333333}
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