5x-1=x^2-10x+25

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Solution for 5x-1=x^2-10x+25 equation: 


Simplifying
5x + -1 = x2 + -10x + 25

Reorder the terms:
-1 + 5x = x2 + -10x + 25

Reorder the terms:
-1 + 5x = 25 + -10x + x2

Solving
-1 + 5x = 25 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
-1 + -25 + 5x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: -1 + -25 = -26
-26 + 5x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 5x + 10x = 15x
-26 + 15x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Reorder the terms:
-26 + 15x + -1x2 = 25 + -25 + -10x + 10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-26 + 15x + -1x2 = 0 + -10x + 10x + x2 + -1x2
-26 + 15x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-26 + 15x + -1x2 = 0 + x2 + -1x2
-26 + 15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-26 + 15x + -1x2 = 0

Factor a trinomial.
(-13 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-13 + x)' equal to zero and attempt to solve:

Simplifying
-13 + x = 0

Solving
-13 + x = 0

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

Add '13' to each side of the equation.
-13 + 13 + x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + x = 0 + 13
x = 0 + 13

Combine like terms: 0 + 13 = 13
x = 13

Simplifying
x = 13

Subproblem 2
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
Solution
x = {13, 2}

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