y=3y^2+2y-4

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Solution for y=3y^2+2y-4 equation: 


Simplifying
y = 3y2 + 2y + -4

Reorder the terms:
y = -4 + 2y + 3y2

Solving
y = -4 + 2y + 3y2

Solving for variable 'y'.

Reorder the terms:
4 + y + -2y + -3y2 = -4 + 2y + 3y2 + 4 + -2y + -3y2

Combine like terms: y + -2y = -1y
4 + -1y + -3y2 = -4 + 2y + 3y2 + 4 + -2y + -3y2

Reorder the terms:
4 + -1y + -3y2 = -4 + 4 + 2y + -2y + 3y2 + -3y2

Combine like terms: -4 + 4 = 0
4 + -1y + -3y2 = 0 + 2y + -2y + 3y2 + -3y2
4 + -1y + -3y2 = 2y + -2y + 3y2 + -3y2

Combine like terms: 2y + -2y = 0
4 + -1y + -3y2 = 0 + 3y2 + -3y2
4 + -1y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
4 + -1y + -3y2 = 0

Factor a trinomial.
(1 + -1y)(4 + 3y) = 0


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

Simplifying
1 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 1

Simplifying
y = 1

Subproblem 2
Set the factor '(4 + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3y = 0

Solving
4 + 3y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3y = 0 + -4
3y = 0 + -4

Combine like terms: 0 + -4 = -4
3y = -4

Divide each side by '3'.
y = -1.333333333

Simplifying
y = -1.333333333
Solution
y = {1, -1.333333333}

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