(6-y)(3y-7)=0

Solution for (6-y)(3y-7)=0 equation:

Simplifying
(6 + -1y)(3y + -7) = 0

Reorder the terms:
(6 + -1y)(-7 + 3y) = 0

Multiply (6 + -1y) * (-7 + 3y)
(6(-7 + 3y) + -1y * (-7 + 3y)) = 0
((-7 * 6 + 3y * 6) + -1y * (-7 + 3y)) = 0
((-42 + 18y) + -1y * (-7 + 3y)) = 0
(-42 + 18y + (-7 * -1y + 3y * -1y)) = 0
(-42 + 18y + (7y + -3y2)) = 0

Combine like terms: 18y + 7y = 25y
(-42 + 25y + -3y2) = 0

Solving
-42 + 25y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + y)(7 + -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 '(7 + -3y)' equal to zero and attempt to solve:

Simplifying
7 + -3y = 0

Solving
7 + -3y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3y = 0 + -7
-3y = 0 + -7

Combine like terms: 0 + -7 = -7
-3y = -7

Divide each side by '-3'.
y = 2.333333333

Simplifying
y = 2.333333333
Solution
y = {6, 2.333333333}