(x-5)*(x-8)=40

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Solution for (x-5)*(x-8)=40 equation: 


Simplifying
(x + -5)(x + -8) = 40

Reorder the terms:
(-5 + x)(x + -8) = 40

Reorder the terms:
(-5 + x)(-8 + x) = 40

Multiply (-5 + x) * (-8 + x)
(-5(-8 + x) + x(-8 + x)) = 40
((-8 * -5 + x * -5) + x(-8 + x)) = 40
((40 + -5x) + x(-8 + x)) = 40
(40 + -5x + (-8 * x + x * x)) = 40
(40 + -5x + (-8x + x2)) = 40

Combine like terms: -5x + -8x = -13x
(40 + -13x + x2) = 40

Add '-40' to each side of the equation.
40 + -13x + -40 + x2 = 40 + -40

Reorder the terms:
40 + -40 + -13x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
0 + -13x + x2 = 40 + -40
-13x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-13x + x2 = 0

Solving
-13x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-13 + 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 '(-13 + x)' equal to zero and attempt to solve:

Simplifying
-13 + x = 0

Solving
-13 + x = 0

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

Add '13' to each side of the equation.
-13 + 13 + x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + x = 0 + 13
x = 0 + 13

Combine like terms: 0 + 13 = 13
x = 13

Simplifying
x = 13
Solution
x = {0, 13}

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