3y^2=12y-5-y^2

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Solution for 3y^2=12y-5-y^2 equation: 


Simplifying
3y2 = 12y + -5 + -1y2

Reorder the terms:
3y2 = -5 + 12y + -1y2

Solving
3y2 = -5 + 12y + -1y2

Solving for variable 'y'.

Reorder the terms:
5 + -12y + 3y2 + y2 = -5 + 12y + -1y2 + 5 + -12y + y2

Combine like terms: 3y2 + y2 = 4y2
5 + -12y + 4y2 = -5 + 12y + -1y2 + 5 + -12y + y2

Reorder the terms:
5 + -12y + 4y2 = -5 + 5 + 12y + -12y + -1y2 + y2

Combine like terms: -5 + 5 = 0
5 + -12y + 4y2 = 0 + 12y + -12y + -1y2 + y2
5 + -12y + 4y2 = 12y + -12y + -1y2 + y2

Combine like terms: 12y + -12y = 0
5 + -12y + 4y2 = 0 + -1y2 + y2
5 + -12y + 4y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
5 + -12y + 4y2 = 0

Factor a trinomial.
(1 + -2y)(5 + -2y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {0.5, 2.5}

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