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Simplifying (1 + 5y)(5y + -1) = 10y + -1 Reorder the terms: (1 + 5y)(-1 + 5y) = 10y + -1 Multiply (1 + 5y) * (-1 + 5y) (1(-1 + 5y) + 5y * (-1 + 5y)) = 10y + -1 ((-1 * 1 + 5y * 1) + 5y * (-1 + 5y)) = 10y + -1 ((-1 + 5y) + 5y * (-1 + 5y)) = 10y + -1 (-1 + 5y + (-1 * 5y + 5y * 5y)) = 10y + -1 (-1 + 5y + (-5y + 25y2)) = 10y + -1 Combine like terms: 5y + -5y = 0 (-1 + 0 + 25y2) = 10y + -1 (-1 + 25y2) = 10y + -1 Reorder the terms: -1 + 25y2 = -1 + 10y Add '1' to each side of the equation. -1 + 1 + 25y2 = -1 + 1 + 10y Combine like terms: -1 + 1 = 0 0 + 25y2 = -1 + 1 + 10y 25y2 = -1 + 1 + 10y Combine like terms: -1 + 1 = 0 25y2 = 0 + 10y 25y2 = 10y Solving 25y2 = 10y Solving for variable 'y'. Reorder the terms: -10y + 25y2 = 10y + -10y Combine like terms: 10y + -10y = 0 -10y + 25y2 = 0 Factor out the Greatest Common Factor (GCF), '5y'. 5y(-2 + 5y) = 0 Ignore the factor 5.Subproblem 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 '(-2 + 5y)' equal to zero and attempt to solve: Simplifying -2 + 5y = 0 Solving -2 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 5y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5y = 0 + 2 5y = 0 + 2 Combine like terms: 0 + 2 = 2 5y = 2 Divide each side by '5'. y = 0.4 Simplifying y = 0.4Solution
y = {0, 0.4}
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