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

Solution for (6-y)(3y-4)=0 equation:

Simplifying
(6 + -1y)(3y + -4) = 0

Reorder the terms:
(6 + -1y)(-4 + 3y) = 0

Multiply (6 + -1y) * (-4 + 3y)
(6(-4 + 3y) + -1y * (-4 + 3y)) = 0
((-4 * 6 + 3y * 6) + -1y * (-4 + 3y)) = 0
((-24 + 18y) + -1y * (-4 + 3y)) = 0
(-24 + 18y + (-4 * -1y + 3y * -1y)) = 0
(-24 + 18y + (4y + -3y2)) = 0

Combine like terms: 18y + 4y = 22y
(-24 + 22y + -3y2) = 0

Solving
-24 + 22y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + y)(4 + -3y) = 0

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

Simplifying
-6 + y = 0

Solving
-6 + y = 0

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

Add '6' to each side of the equation.
-6 + 6 + y = 0 + 6

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

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

Simplifying
y = 6
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 = {6, 1.333333333}