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Simplifying 6y(3y + -2) + (3y + -2) = 0 Reorder the terms: 6y(-2 + 3y) + (3y + -2) = 0 (-2 * 6y + 3y * 6y) + (3y + -2) = 0 (-12y + 18y2) + (3y + -2) = 0 Reorder the terms: -12y + 18y2 + (-2 + 3y) = 0 Remove parenthesis around (-2 + 3y) -12y + 18y2 + -2 + 3y = 0 Reorder the terms: -2 + -12y + 3y + 18y2 = 0 Combine like terms: -12y + 3y = -9y -2 + -9y + 18y2 = 0 Solving -2 + -9y + 18y2 = 0 Solving for variable 'y'. Factor a trinomial. (-1 + -6y)(2 + -3y) = 0Subproblem 1
Set the factor '(-1 + -6y)' equal to zero and attempt to solve: Simplifying -1 + -6y = 0 Solving -1 + -6y = 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 + -6y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6y = 0 + 1 -6y = 0 + 1 Combine like terms: 0 + 1 = 1 -6y = 1 Divide each side by '-6'. y = -0.1666666667 Simplifying y = -0.1666666667Subproblem 2
Set the factor '(2 + -3y)' equal to zero and attempt to solve: Simplifying 2 + -3y = 0 Solving 2 + -3y = 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 + -3y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3y = 0 + -2 -3y = 0 + -2 Combine like terms: 0 + -2 = -2 -3y = -2 Divide each side by '-3'. y = 0.6666666667 Simplifying y = 0.6666666667Solution
y = {-0.1666666667, 0.6666666667}
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