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

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

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

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

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

Multiply (-4 + y) * (-3 + y)
(-4(-3 + y) + y(-3 + y)) = 6
((-3 * -4 + y * -4) + y(-3 + y)) = 6
((12 + -4y) + y(-3 + y)) = 6
(12 + -4y + (-3 * y + y * y)) = 6
(12 + -4y + (-3y + y2)) = 6

Combine like terms: -4y + -3y = -7y
(12 + -7y + y2) = 6

Solving
12 + -7y + y2 = 6

Solving for variable 'y'.

Reorder the terms:
12 + -6 + -7y + y2 = 6 + -6

Combine like terms: 12 + -6 = 6
6 + -7y + y2 = 6 + -6

Combine like terms: 6 + -6 = 0
6 + -7y + y2 = 0

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

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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 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 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {1, 6}