4y(3y+2)=(3y+2)

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Solution for 4y(3y+2)=(3y+2) equation: 


Simplifying
4y(3y + 2) = (3y + 2)

Reorder the terms:
4y(2 + 3y) = (3y + 2)
(2 * 4y + 3y * 4y) = (3y + 2)
(8y + 12y2) = (3y + 2)

Reorder the terms:
8y + 12y2 = (2 + 3y)

Remove parenthesis around (2 + 3y)
8y + 12y2 = 2 + 3y

Solving
8y + 12y2 = 2 + 3y

Solving for variable 'y'.

Reorder the terms:
-2 + 8y + -3y + 12y2 = 2 + 3y + -2 + -3y

Combine like terms: 8y + -3y = 5y
-2 + 5y + 12y2 = 2 + 3y + -2 + -3y

Reorder the terms:
-2 + 5y + 12y2 = 2 + -2 + 3y + -3y

Combine like terms: 2 + -2 = 0
-2 + 5y + 12y2 = 0 + 3y + -3y
-2 + 5y + 12y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-2 + 5y + 12y2 = 0

Factor a trinomial.
(-2 + -3y)(1 + -4y) = 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 + -4y)' equal to zero and attempt to solve:

Simplifying
1 + -4y = 0

Solving
1 + -4y = 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 + -4y = 0 + -1

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

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

Divide each side by '-4'.
y = 0.25

Simplifying
y = 0.25
Solution
y = {-0.6666666667, 0.25}

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