10x^2-50+x=500x

Solution for 10x^2-50+x=500x equation:

Simplifying
10x2 + -50 + x = 500x

Reorder the terms:
-50 + x + 10x2 = 500x

Solving
-50 + x + 10x2 = 500x

Solving for variable 'x'.

Reorder the terms:
-50 + x + -500x + 10x2 = 500x + -500x

Combine like terms: x + -500x = -499x
-50 + -499x + 10x2 = 500x + -500x

Combine like terms: 500x + -500x = 0
-50 + -499x + 10x2 = 0

Factor a trinomial.
(-1 + -10x)(50 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -10x)' equal to zero and attempt to solve:

Simplifying
-1 + -10x = 0

Solving
-1 + -10x = 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 + -10x = 0 + 1

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

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

Divide each side by '-10'.
x = -0.1

Simplifying
x = -0.1
Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Solution
x = {-0.1, 50}