-3(y-4)(-y+3)=0

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

Simplifying
-3(y + -4)(-1y + 3) = 0

Reorder the terms:
-3(-4 + y)(-1y + 3) = 0

Reorder the terms:
-3(-4 + y)(3 + -1y) = 0

Multiply (-4 + y) * (3 + -1y)
-3(-4(3 + -1y) + y(3 + -1y)) = 0
-3((3 * -4 + -1y * -4) + y(3 + -1y)) = 0
-3((-12 + 4y) + y(3 + -1y)) = 0
-3(-12 + 4y + (3 * y + -1y * y)) = 0
-3(-12 + 4y + (3y + -1y2)) = 0

Combine like terms: 4y + 3y = 7y
-3(-12 + 7y + -1y2) = 0
(-12 * -3 + 7y * -3 + -1y2 * -3) = 0
(36 + -21y + 3y2) = 0

Solving
36 + -21y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -7y + y2) = 0

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

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

Simplifying
4 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {3, 4}