(x-8)(x-2)=-5

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Solution for (x-8)(x-2)=-5 equation: 


Simplifying
(x + -8)(x + -2) = -5

Reorder the terms:
(-8 + x)(x + -2) = -5

Reorder the terms:
(-8 + x)(-2 + x) = -5

Multiply (-8 + x) * (-2 + x)
(-8(-2 + x) + x(-2 + x)) = -5
((-2 * -8 + x * -8) + x(-2 + x)) = -5
((16 + -8x) + x(-2 + x)) = -5
(16 + -8x + (-2 * x + x * x)) = -5
(16 + -8x + (-2x + x2)) = -5

Combine like terms: -8x + -2x = -10x
(16 + -10x + x2) = -5

Solving
16 + -10x + x2 = -5

Solving for variable 'x'.

Reorder the terms:
16 + 5 + -10x + x2 = -5 + 5

Combine like terms: 16 + 5 = 21
21 + -10x + x2 = -5 + 5

Combine like terms: -5 + 5 = 0
21 + -10x + x2 = 0

Factor a trinomial.
(3 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {3, 7}

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