(x-4)(x-5)=12

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Solution for (x-4)(x-5)=12 equation: 


Simplifying
(x + -4)(x + -5) = 12

Reorder the terms:
(-4 + x)(x + -5) = 12

Reorder the terms:
(-4 + x)(-5 + x) = 12

Multiply (-4 + x) * (-5 + x)
(-4(-5 + x) + x(-5 + x)) = 12
((-5 * -4 + x * -4) + x(-5 + x)) = 12
((20 + -4x) + x(-5 + x)) = 12
(20 + -4x + (-5 * x + x * x)) = 12
(20 + -4x + (-5x + x2)) = 12

Combine like terms: -4x + -5x = -9x
(20 + -9x + x2) = 12

Solving
20 + -9x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
20 + -12 + -9x + x2 = 12 + -12

Combine like terms: 20 + -12 = 8
8 + -9x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
8 + -9x + 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}

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