4y(3y-1)=-9y+3

Solution for 4y(3y-1)=-9y+3 equation:

Simplifying
4y(3y + -1) = -9y + 3

Reorder the terms:
4y(-1 + 3y) = -9y + 3
(-1 * 4y + 3y * 4y) = -9y + 3
(-4y + 12y2) = -9y + 3

Reorder the terms:
-4y + 12y2 = 3 + -9y

Solving
-4y + 12y2 = 3 + -9y

Solving for variable 'y'.

Reorder the terms:
-3 + -4y + 9y + 12y2 = 3 + -9y + -3 + 9y

Combine like terms: -4y + 9y = 5y
-3 + 5y + 12y2 = 3 + -9y + -3 + 9y

Reorder the terms:
-3 + 5y + 12y2 = 3 + -3 + -9y + 9y

Combine like terms: 3 + -3 = 0
-3 + 5y + 12y2 = 0 + -9y + 9y
-3 + 5y + 12y2 = -9y + 9y

Combine like terms: -9y + 9y = 0
-3 + 5y + 12y2 = 0

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

Subproblem 1
Set the factor '(-3 + -4y)' equal to zero and attempt to solve:

Simplifying
-3 + -4y = 0

Solving
-3 + -4y = 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 + -4y = 0 + 3

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

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

Divide each side by '-4'.
y = -0.75

Simplifying
y = -0.75
Subproblem 2
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
Solution
y = {-0.75, 0.3333333333}