x^2-4x+10=8x-x^2

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Solution for x^2-4x+10=8x-x^2 equation: 


Simplifying
x2 + -4x + 10 = 8x + -1x2

Reorder the terms:
10 + -4x + x2 = 8x + -1x2

Solving
10 + -4x + x2 = 8x + -1x2

Solving for variable 'x'.

Reorder the terms:
10 + -4x + -8x + x2 + x2 = 8x + -1x2 + -8x + x2

Combine like terms: -4x + -8x = -12x
10 + -12x + x2 + x2 = 8x + -1x2 + -8x + x2

Combine like terms: x2 + x2 = 2x2
10 + -12x + 2x2 = 8x + -1x2 + -8x + x2

Reorder the terms:
10 + -12x + 2x2 = 8x + -8x + -1x2 + x2

Combine like terms: 8x + -8x = 0
10 + -12x + 2x2 = 0 + -1x2 + x2
10 + -12x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
10 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6x + x2) = 0

Factor a trinomial.
2((1 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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