(x-8)(x-5)=4

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Solution for (x-8)(x-5)=4 equation: 


Simplifying
(x + -8)(x + -5) = 4

Reorder the terms:
(-8 + x)(x + -5) = 4

Reorder the terms:
(-8 + x)(-5 + x) = 4

Multiply (-8 + x) * (-5 + x)
(-8(-5 + x) + x(-5 + x)) = 4
((-5 * -8 + x * -8) + x(-5 + x)) = 4
((40 + -8x) + x(-5 + x)) = 4
(40 + -8x + (-5 * x + x * x)) = 4
(40 + -8x + (-5x + x2)) = 4

Combine like terms: -8x + -5x = -13x
(40 + -13x + x2) = 4

Solving
40 + -13x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
40 + -4 + -13x + x2 = 4 + -4

Combine like terms: 40 + -4 = 36
36 + -13x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
36 + -13x + x2 = 0

Factor a trinomial.
(4 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {4, 9}

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