3x+13=x^2-10x+25

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Solution for 3x+13=x^2-10x+25 equation: 


Simplifying
3x + 13 = x2 + -10x + 25

Reorder the terms:
13 + 3x = x2 + -10x + 25

Reorder the terms:
13 + 3x = 25 + -10x + x2

Solving
13 + 3x = 25 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
13 + -25 + 3x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 13 + -25 = -12
-12 + 3x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 3x + 10x = 13x
-12 + 13x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Reorder the terms:
-12 + 13x + -1x2 = 25 + -25 + -10x + 10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-12 + 13x + -1x2 = 0 + -10x + 10x + x2 + -1x2
-12 + 13x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-12 + 13x + -1x2 = 0 + x2 + -1x2
-12 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 13x + -1x2 = 0

Factor a trinomial.
(-12 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve:

Simplifying
-12 + x = 0

Solving
-12 + x = 0

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + x = 0 + 12
x = 0 + 12

Combine like terms: 0 + 12 = 12
x = 12

Simplifying
x = 12

Subproblem 2
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
Solution
x = {12, 1}

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