y(6y-42)-9(6y-42)=0

Solution for y(6y-42)-9(6y-42)=0 equation:

Simplifying
y(6y + -42) + -9(6y + -42) = 0

Reorder the terms:
y(-42 + 6y) + -9(6y + -42) = 0
(-42 * y + 6y * y) + -9(6y + -42) = 0
(-42y + 6y2) + -9(6y + -42) = 0

Reorder the terms:
-42y + 6y2 + -9(-42 + 6y) = 0
-42y + 6y2 + (-42 * -9 + 6y * -9) = 0
-42y + 6y2 + (378 + -54y) = 0

Reorder the terms:
378 + -42y + -54y + 6y2 = 0

Combine like terms: -42y + -54y = -96y
378 + -96y + 6y2 = 0

Solving
378 + -96y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(63 + -16y + y2) = 0

Factor a trinomial.
6((7 + -1y)(9 + -1y)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Subproblem 2
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {7, 9}