(x-3)(x-4)=20

Solution for (x-3)(x-4)=20 equation:

Simplifying
(x + -3)(x + -4) = 20

Reorder the terms:
(-3 + x)(x + -4) = 20

Reorder the terms:
(-3 + x)(-4 + x) = 20

Multiply (-3 + x) * (-4 + x)
(-3(-4 + x) + x(-4 + x)) = 20
((-4 * -3 + x * -3) + x(-4 + x)) = 20
((12 + -3x) + x(-4 + x)) = 20
(12 + -3x + (-4 * x + x * x)) = 20
(12 + -3x + (-4x + x2)) = 20

Combine like terms: -3x + -4x = -7x
(12 + -7x + x2) = 20

Solving
12 + -7x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
12 + -20 + -7x + x2 = 20 + -20

Combine like terms: 12 + -20 = -8
-8 + -7x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-8 + -7x + x2 = 0

Factor a trinomial.
(-1 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1, 8}