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Simplifying 20y2 + 3y = 5y2 + 5y + 1 Reorder the terms: 3y + 20y2 = 5y2 + 5y + 1 Reorder the terms: 3y + 20y2 = 1 + 5y + 5y2 Solving 3y + 20y2 = 1 + 5y + 5y2 Solving for variable 'y'. Reorder the terms: -1 + 3y + -5y + 20y2 + -5y2 = 1 + 5y + 5y2 + -1 + -5y + -5y2 Combine like terms: 3y + -5y = -2y -1 + -2y + 20y2 + -5y2 = 1 + 5y + 5y2 + -1 + -5y + -5y2 Combine like terms: 20y2 + -5y2 = 15y2 -1 + -2y + 15y2 = 1 + 5y + 5y2 + -1 + -5y + -5y2 Reorder the terms: -1 + -2y + 15y2 = 1 + -1 + 5y + -5y + 5y2 + -5y2 Combine like terms: 1 + -1 = 0 -1 + -2y + 15y2 = 0 + 5y + -5y + 5y2 + -5y2 -1 + -2y + 15y2 = 5y + -5y + 5y2 + -5y2 Combine like terms: 5y + -5y = 0 -1 + -2y + 15y2 = 0 + 5y2 + -5y2 -1 + -2y + 15y2 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 -1 + -2y + 15y2 = 0 Factor a trinomial. (-1 + -5y)(1 + -3y) = 0Subproblem 1
Set the factor '(-1 + -5y)' equal to zero and attempt to solve: Simplifying -1 + -5y = 0 Solving -1 + -5y = 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 + -5y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5y = 0 + 1 -5y = 0 + 1 Combine like terms: 0 + 1 = 1 -5y = 1 Divide each side by '-5'. y = -0.2 Simplifying y = -0.2Subproblem 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 = {-0.2, 0.3333333333}
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