3y^2+8y=12y+15

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Solution for 3y^2+8y=12y+15 equation: 


Simplifying
3y2 + 8y = 12y + 15

Reorder the terms:
8y + 3y2 = 12y + 15

Reorder the terms:
8y + 3y2 = 15 + 12y

Solving
8y + 3y2 = 15 + 12y

Solving for variable 'y'.

Reorder the terms:
-15 + 8y + -12y + 3y2 = 15 + 12y + -15 + -12y

Combine like terms: 8y + -12y = -4y
-15 + -4y + 3y2 = 15 + 12y + -15 + -12y

Reorder the terms:
-15 + -4y + 3y2 = 15 + -15 + 12y + -12y

Combine like terms: 15 + -15 = 0
-15 + -4y + 3y2 = 0 + 12y + -12y
-15 + -4y + 3y2 = 12y + -12y

Combine like terms: 12y + -12y = 0
-15 + -4y + 3y2 = 0

Factor a trinomial.
(-5 + -3y)(3 + -1y) = 0


Subproblem 1
Set the factor '(-5 + -3y)' equal to zero and attempt to solve:

Simplifying
-5 + -3y = 0

Solving
-5 + -3y = 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 + -3y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3y = 0 + 5
-3y = 0 + 5

Combine like terms: 0 + 5 = 5
-3y = 5

Divide each side by '-3'.
y = -1.666666667

Simplifying
y = -1.666666667

Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-1.666666667, 3}

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