4(3y^2-7y+4)=0

Solution for 4(3y^2-7y+4)=0 equation:

Simplifying
4(3y2 + -7y + 4) = 0

Reorder the terms:
4(4 + -7y + 3y2) = 0
(4 * 4 + -7y * 4 + 3y2 * 4) = 0
(16 + -28y + 12y2) = 0

Solving
16 + -28y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -7y + 3y2) = 0

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

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Subproblem 2
Set the factor '(4 + -3y)' equal to zero and attempt to solve:

Simplifying
4 + -3y = 0

Solving
4 + -3y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3y = 0 + -4

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

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

Divide each side by '-3'.
y = 1.333333333

Simplifying
y = 1.333333333
Solution
y = {1, 1.333333333}