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Simplifying 2y(4y + 5) = 4y + -1 Reorder the terms: 2y(5 + 4y) = 4y + -1 (5 * 2y + 4y * 2y) = 4y + -1 (10y + 8y2) = 4y + -1 Reorder the terms: 10y + 8y2 = -1 + 4y Solving 10y + 8y2 = -1 + 4y Solving for variable 'y'. Reorder the terms: 1 + 10y + -4y + 8y2 = -1 + 4y + 1 + -4y Combine like terms: 10y + -4y = 6y 1 + 6y + 8y2 = -1 + 4y + 1 + -4y Reorder the terms: 1 + 6y + 8y2 = -1 + 1 + 4y + -4y Combine like terms: -1 + 1 = 0 1 + 6y + 8y2 = 0 + 4y + -4y 1 + 6y + 8y2 = 4y + -4y Combine like terms: 4y + -4y = 0 1 + 6y + 8y2 = 0 Factor a trinomial. (1 + 2y)(1 + 4y) = 0Subproblem 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 + 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 = {-0.5, -0.25}
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