4(3y^2-7y+4)=1

Solution for 4(3y^2-7y+4)=1 equation:

Simplifying
4(3y2 + -7y + 4) = 1

Reorder the terms:
4(4 + -7y + 3y2) = 1
(4 * 4 + -7y * 4 + 3y2 * 4) = 1
(16 + -28y + 12y2) = 1

Solving
16 + -28y + 12y2 = 1

Solving for variable 'y'.

Reorder the terms:
16 + -1 + -28y + 12y2 = 1 + -1

Combine like terms: 16 + -1 = 15
15 + -28y + 12y2 = 1 + -1

Combine like terms: 1 + -1 = 0
15 + -28y + 12y2 = 0

Factor a trinomial.
(5 + -6y)(3 + -2y) = 0

Subproblem 1
Set the factor '(5 + -6y)' equal to zero and attempt to solve:

Simplifying
5 + -6y = 0

Solving
5 + -6y = 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 + -6y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6y = 0 + -5
-6y = 0 + -5

Combine like terms: 0 + -5 = -5
-6y = -5

Divide each side by '-6'.
y = 0.8333333333

Simplifying
y = 0.8333333333
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 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 + -2y = 0 + -3

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

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

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {0.8333333333, 1.5}