(x-5)(x-7)=8

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Solution for (x-5)(x-7)=8 equation: 


Simplifying
(x + -5)(x + -7) = 8

Reorder the terms:
(-5 + x)(x + -7) = 8

Reorder the terms:
(-5 + x)(-7 + x) = 8

Multiply (-5 + x) * (-7 + x)
(-5(-7 + x) + x(-7 + x)) = 8
((-7 * -5 + x * -5) + x(-7 + x)) = 8
((35 + -5x) + x(-7 + x)) = 8
(35 + -5x + (-7 * x + x * x)) = 8
(35 + -5x + (-7x + x2)) = 8

Combine like terms: -5x + -7x = -12x
(35 + -12x + x2) = 8

Solving
35 + -12x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
35 + -8 + -12x + x2 = 8 + -8

Combine like terms: 35 + -8 = 27
27 + -12x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
27 + -12x + x2 = 0

Factor a trinomial.
(3 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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 = {3, 9}

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