x^2-2x+13=10x-7

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Solution for x^2-2x+13=10x-7 equation: 


Simplifying
x2 + -2x + 13 = 10x + -7

Reorder the terms:
13 + -2x + x2 = 10x + -7

Reorder the terms:
13 + -2x + x2 = -7 + 10x

Solving
13 + -2x + x2 = -7 + 10x

Solving for variable 'x'.

Reorder the terms:
13 + 7 + -2x + -10x + x2 = -7 + 10x + 7 + -10x

Combine like terms: 13 + 7 = 20
20 + -2x + -10x + x2 = -7 + 10x + 7 + -10x

Combine like terms: -2x + -10x = -12x
20 + -12x + x2 = -7 + 10x + 7 + -10x

Reorder the terms:
20 + -12x + x2 = -7 + 7 + 10x + -10x

Combine like terms: -7 + 7 = 0
20 + -12x + x2 = 0 + 10x + -10x
20 + -12x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
20 + -12x + x2 = 0

Factor a trinomial.
(2 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {2, 10}

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