3x+10=x^2-20x+100

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Solution for 3x+10=x^2-20x+100 equation: 


Simplifying
3x + 10 = x2 + -20x + 100

Reorder the terms:
10 + 3x = x2 + -20x + 100

Reorder the terms:
10 + 3x = 100 + -20x + x2

Solving
10 + 3x = 100 + -20x + x2

Solving for variable 'x'.

Reorder the terms:
10 + -100 + 3x + 20x + -1x2 = 100 + -20x + x2 + -100 + 20x + -1x2

Combine like terms: 10 + -100 = -90
-90 + 3x + 20x + -1x2 = 100 + -20x + x2 + -100 + 20x + -1x2

Combine like terms: 3x + 20x = 23x
-90 + 23x + -1x2 = 100 + -20x + x2 + -100 + 20x + -1x2

Reorder the terms:
-90 + 23x + -1x2 = 100 + -100 + -20x + 20x + x2 + -1x2

Combine like terms: 100 + -100 = 0
-90 + 23x + -1x2 = 0 + -20x + 20x + x2 + -1x2
-90 + 23x + -1x2 = -20x + 20x + x2 + -1x2

Combine like terms: -20x + 20x = 0
-90 + 23x + -1x2 = 0 + x2 + -1x2
-90 + 23x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-90 + 23x + -1x2 = 0

Factor a trinomial.
(-18 + x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-18 + x)' equal to zero and attempt to solve:

Simplifying
-18 + x = 0

Solving
-18 + x = 0

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

Add '18' to each side of the equation.
-18 + 18 + x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + x = 0 + 18
x = 0 + 18

Combine like terms: 0 + 18 = 18
x = 18

Simplifying
x = 18

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 = {18, 5}

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