19x-20=x^2+10x

Solution for 19x-20=x^2+10x equation:

Simplifying
19x + -20 = x2 + 10x

Reorder the terms:
-20 + 19x = x2 + 10x

Reorder the terms:
-20 + 19x = 10x + x2

Solving
-20 + 19x = 10x + x2

Solving for variable 'x'.

Combine like terms: 19x + -10x = 9x
-20 + 9x + -1x2 = 10x + x2 + -10x + -1x2

Reorder the terms:
-20 + 9x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-20 + 9x + -1x2 = 0 + x2 + -1x2
-20 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + 9x + -1x2 = 0

Factor a trinomial.
(-5 + x)(4 + -1x) = 0

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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {5, 4}