9y^2=6y-1

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Solution for 9y^2=6y-1 equation:


Simplifying
9y2 = 6y + -1

Reorder the terms:
9y2 = -1 + 6y

Solving
9y2 = -1 + 6y

Solving for variable 'y'.

Reorder the terms:
1 + -6y + 9y2 = -1 + 6y + 1 + -6y

Reorder the terms:
1 + -6y + 9y2 = -1 + 1 + 6y + -6y

Combine like terms: -1 + 1 = 0
1 + -6y + 9y2 = 0 + 6y + -6y
1 + -6y + 9y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
1 + -6y + 9y2 = 0

Factor a trinomial.
(1 + -3y)(1 + -3y) = 0

Subproblem 1

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 = 0.3333333333

Subproblem 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 = 0.3333333333

Solution

y = {0.3333333333, 0.3333333333}

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