(x-3)(x-4)=6

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

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

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

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

Multiply (-3 + x) * (-4 + x)
(-3(-4 + x) + x(-4 + x)) = 6
((-4 * -3 + x * -3) + x(-4 + x)) = 6
((12 + -3x) + x(-4 + x)) = 6
(12 + -3x + (-4 * x + x * x)) = 6
(12 + -3x + (-4x + x2)) = 6

Combine like terms: -3x + -4x = -7x
(12 + -7x + x2) = 6

Solving
12 + -7x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
12 + -6 + -7x + x2 = 6 + -6

Combine like terms: 12 + -6 = 6
6 + -7x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
6 + -7x + x2 = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

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

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