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Simplifying (2y + 3)(4y + -2) = 0 Reorder the terms: (3 + 2y)(4y + -2) = 0 Reorder the terms: (3 + 2y)(-2 + 4y) = 0 Multiply (3 + 2y) * (-2 + 4y) (3(-2 + 4y) + 2y * (-2 + 4y)) = 0 ((-2 * 3 + 4y * 3) + 2y * (-2 + 4y)) = 0 ((-6 + 12y) + 2y * (-2 + 4y)) = 0 (-6 + 12y + (-2 * 2y + 4y * 2y)) = 0 (-6 + 12y + (-4y + 8y2)) = 0 Combine like terms: 12y + -4y = 8y (-6 + 8y + 8y2) = 0 Solving -6 + 8y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4y + 4y2) = 0 Factor a trinomial. 2((-3 + -2y)(1 + -2y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve: Simplifying -3 + -2y = 0 Solving -3 + -2y = 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 + -2y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2y = 0 + 3 -2y = 0 + 3 Combine like terms: 0 + 3 = 3 -2y = 3 Divide each side by '-2'. y = -1.5 Simplifying y = -1.5Subproblem 2
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 = 0.5Solution
y = {-1.5, 0.5}
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