y^2-3y+2=4y-2y^2

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


Simplifying
y2 + -3y + 2 = 4y + -2y2

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

Solving
2 + -3y + y2 = 4y + -2y2

Solving for variable 'y'.

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

Combine like terms: -3y + -4y = -7y
2 + -7y + y2 + 2y2 = 4y + -2y2 + -4y + 2y2

Combine like terms: y2 + 2y2 = 3y2
2 + -7y + 3y2 = 4y + -2y2 + -4y + 2y2

Reorder the terms:
2 + -7y + 3y2 = 4y + -4y + -2y2 + 2y2

Combine like terms: 4y + -4y = 0
2 + -7y + 3y2 = 0 + -2y2 + 2y2
2 + -7y + 3y2 = -2y2 + 2y2

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

Factor a trinomial.
(1 + -3y)(2 + -1y) = 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 '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {0.3333333333, 2}

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