(x-8)(x-10)=5x+38

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Solution for (x-8)(x-10)=5x+38 equation: 


Simplifying
(x + -8)(x + -10) = 5x + 38

Reorder the terms:
(-8 + x)(x + -10) = 5x + 38

Reorder the terms:
(-8 + x)(-10 + x) = 5x + 38

Multiply (-8 + x) * (-10 + x)
(-8(-10 + x) + x(-10 + x)) = 5x + 38
((-10 * -8 + x * -8) + x(-10 + x)) = 5x + 38
((80 + -8x) + x(-10 + x)) = 5x + 38
(80 + -8x + (-10 * x + x * x)) = 5x + 38
(80 + -8x + (-10x + x2)) = 5x + 38

Combine like terms: -8x + -10x = -18x
(80 + -18x + x2) = 5x + 38

Reorder the terms:
80 + -18x + x2 = 38 + 5x

Solving
80 + -18x + x2 = 38 + 5x

Solving for variable 'x'.

Reorder the terms:
80 + -38 + -18x + -5x + x2 = 38 + 5x + -38 + -5x

Combine like terms: 80 + -38 = 42
42 + -18x + -5x + x2 = 38 + 5x + -38 + -5x

Combine like terms: -18x + -5x = -23x
42 + -23x + x2 = 38 + 5x + -38 + -5x

Reorder the terms:
42 + -23x + x2 = 38 + -38 + 5x + -5x

Combine like terms: 38 + -38 = 0
42 + -23x + x2 = 0 + 5x + -5x
42 + -23x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
42 + -23x + x2 = 0

Factor a trinomial.
(2 + -1x)(21 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {2, 21}

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