9y^2+y-1=3y^2-6y-3

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Solution for 9y^2+y-1=3y^2-6y-3 equation: 


Simplifying
9y2 + y + -1 = 3y2 + -6y + -3

Reorder the terms:
-1 + y + 9y2 = 3y2 + -6y + -3

Reorder the terms:
-1 + y + 9y2 = -3 + -6y + 3y2

Solving
-1 + y + 9y2 = -3 + -6y + 3y2

Solving for variable 'y'.

Reorder the terms:
-1 + 3 + y + 6y + 9y2 + -3y2 = -3 + -6y + 3y2 + 3 + 6y + -3y2

Combine like terms: -1 + 3 = 2
2 + y + 6y + 9y2 + -3y2 = -3 + -6y + 3y2 + 3 + 6y + -3y2

Combine like terms: y + 6y = 7y
2 + 7y + 9y2 + -3y2 = -3 + -6y + 3y2 + 3 + 6y + -3y2

Combine like terms: 9y2 + -3y2 = 6y2
2 + 7y + 6y2 = -3 + -6y + 3y2 + 3 + 6y + -3y2

Reorder the terms:
2 + 7y + 6y2 = -3 + 3 + -6y + 6y + 3y2 + -3y2

Combine like terms: -3 + 3 = 0
2 + 7y + 6y2 = 0 + -6y + 6y + 3y2 + -3y2
2 + 7y + 6y2 = -6y + 6y + 3y2 + -3y2

Combine like terms: -6y + 6y = 0
2 + 7y + 6y2 = 0 + 3y2 + -3y2
2 + 7y + 6y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
2 + 7y + 6y2 = 0

Factor a trinomial.
(2 + 3y)(1 + 2y) = 0


Subproblem 1
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 = -0.6666666667

Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {-0.6666666667, -0.5}

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