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Simplifying y(3y + 1)(4y + -1) = 0 Reorder the terms: y(1 + 3y)(4y + -1) = 0 Reorder the terms: y(1 + 3y)(-1 + 4y) = 0 Multiply (1 + 3y) * (-1 + 4y) y(1(-1 + 4y) + 3y * (-1 + 4y)) = 0 y((-1 * 1 + 4y * 1) + 3y * (-1 + 4y)) = 0 y((-1 + 4y) + 3y * (-1 + 4y)) = 0 y(-1 + 4y + (-1 * 3y + 4y * 3y)) = 0 y(-1 + 4y + (-3y + 12y2)) = 0 Combine like terms: 4y + -3y = 1y y(-1 + 1y + 12y2) = 0 (-1 * y + 1y * y + 12y2 * y) = 0 (-1y + 1y2 + 12y3) = 0 Solving -1y + 1y2 + 12y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-1 + y + 12y2) = 0 Factor a trinomial. y((-1 + -3y)(1 + -4y)) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 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 = -0.3333333333Subproblem 3
Set the factor '(1 + -4y)' equal to zero and attempt to solve: Simplifying 1 + -4y = 0 Solving 1 + -4y = 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 + -4y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4y = 0 + -1 -4y = 0 + -1 Combine like terms: 0 + -1 = -1 -4y = -1 Divide each side by '-4'. y = 0.25 Simplifying y = 0.25Solution
y = {0, -0.3333333333, 0.25}
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