(x-4)(x-5)=20

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Solution for (x-4)(x-5)=20 equation: 


Simplifying
(x + -4)(x + -5) = 20

Reorder the terms:
(-4 + x)(x + -5) = 20

Reorder the terms:
(-4 + x)(-5 + x) = 20

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

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

Add '-20' to each side of the equation.
20 + -9x + -20 + x2 = 20 + -20

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

Combine like terms: 20 + -20 = 0
0 + -9x + x2 = 20 + -20
-9x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-9x + x2 = 0

Solving
-9x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

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

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9
Solution
x = {0, 9}

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