x^2-2x-8=5(x-4)

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Solution for x^2-2x-8=5(x-4) equation: 


Simplifying
x2 + -2x + -8 = 5(x + -4)

Reorder the terms:
-8 + -2x + x2 = 5(x + -4)

Reorder the terms:
-8 + -2x + x2 = 5(-4 + x)
-8 + -2x + x2 = (-4 * 5 + x * 5)
-8 + -2x + x2 = (-20 + 5x)

Solving
-8 + -2x + x2 = -20 + 5x

Solving for variable 'x'.

Reorder the terms:
-8 + 20 + -2x + -5x + x2 = -20 + 5x + 20 + -5x

Combine like terms: -8 + 20 = 12
12 + -2x + -5x + x2 = -20 + 5x + 20 + -5x

Combine like terms: -2x + -5x = -7x
12 + -7x + x2 = -20 + 5x + 20 + -5x

Reorder the terms:
12 + -7x + x2 = -20 + 20 + 5x + -5x

Combine like terms: -20 + 20 = 0
12 + -7x + x2 = 0 + 5x + -5x
12 + -7x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
12 + -7x + x2 = 0

Factor a trinomial.
(3 + -1x)(4 + -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 '(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
Solution
x = {3, 4}

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