(x-5)(x-8)=0

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Solution for (x-5)(x-8)=0 equation: 


Simplifying
(x + -5)(x + -8) = 0

Reorder the terms:
(-5 + x)(x + -8) = 0

Reorder the terms:
(-5 + x)(-8 + x) = 0

Multiply (-5 + x) * (-8 + x)
(-5(-8 + x) + x(-8 + x)) = 0
((-8 * -5 + x * -5) + x(-8 + x)) = 0
((40 + -5x) + x(-8 + x)) = 0
(40 + -5x + (-8 * x + x * x)) = 0
(40 + -5x + (-8x + x2)) = 0

Combine like terms: -5x + -8x = -13x
(40 + -13x + x2) = 0

Solving
40 + -13x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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 = {5, 8}

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