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Simplifying 6y2 + 7y + -3 = -12y2 + -54y + 4 Reorder the terms: -3 + 7y + 6y2 = -12y2 + -54y + 4 Reorder the terms: -3 + 7y + 6y2 = 4 + -54y + -12y2 Solving -3 + 7y + 6y2 = 4 + -54y + -12y2 Solving for variable 'y'. Reorder the terms: -3 + -4 + 7y + 54y + 6y2 + 12y2 = 4 + -54y + -12y2 + -4 + 54y + 12y2 Combine like terms: -3 + -4 = -7 -7 + 7y + 54y + 6y2 + 12y2 = 4 + -54y + -12y2 + -4 + 54y + 12y2 Combine like terms: 7y + 54y = 61y -7 + 61y + 6y2 + 12y2 = 4 + -54y + -12y2 + -4 + 54y + 12y2 Combine like terms: 6y2 + 12y2 = 18y2 -7 + 61y + 18y2 = 4 + -54y + -12y2 + -4 + 54y + 12y2 Reorder the terms: -7 + 61y + 18y2 = 4 + -4 + -54y + 54y + -12y2 + 12y2 Combine like terms: 4 + -4 = 0 -7 + 61y + 18y2 = 0 + -54y + 54y + -12y2 + 12y2 -7 + 61y + 18y2 = -54y + 54y + -12y2 + 12y2 Combine like terms: -54y + 54y = 0 -7 + 61y + 18y2 = 0 + -12y2 + 12y2 -7 + 61y + 18y2 = -12y2 + 12y2 Combine like terms: -12y2 + 12y2 = 0 -7 + 61y + 18y2 = 0 Factor a trinomial. (-7 + -2y)(1 + -9y) = 0Subproblem 1
Set the factor '(-7 + -2y)' equal to zero and attempt to solve: Simplifying -7 + -2y = 0 Solving -7 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2y = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2y = 0 + 7 -2y = 0 + 7 Combine like terms: 0 + 7 = 7 -2y = 7 Divide each side by '-2'. y = -3.5 Simplifying y = -3.5Subproblem 2
Set the factor '(1 + -9y)' equal to zero and attempt to solve: Simplifying 1 + -9y = 0 Solving 1 + -9y = 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 + -9y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9y = 0 + -1 -9y = 0 + -1 Combine like terms: 0 + -1 = -1 -9y = -1 Divide each side by '-9'. y = 0.1111111111 Simplifying y = 0.1111111111Solution
y = {-3.5, 0.1111111111}
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