150x-x^2=500+90x

Solution for 150x-x^2=500+90x equation:

Simplifying
150x + -1x2 = 500 + 90x

Solving
150x + -1x2 = 500 + 90x

Solving for variable 'x'.

Reorder the terms:
-500 + 150x + -90x + -1x2 = 500 + 90x + -500 + -90x

Combine like terms: 150x + -90x = 60x
-500 + 60x + -1x2 = 500 + 90x + -500 + -90x

Reorder the terms:
-500 + 60x + -1x2 = 500 + -500 + 90x + -90x

Combine like terms: 500 + -500 = 0
-500 + 60x + -1x2 = 0 + 90x + -90x
-500 + 60x + -1x2 = 90x + -90x

Combine like terms: 90x + -90x = 0
-500 + 60x + -1x2 = 0

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

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

Simplifying
-50 + x = 0

Solving
-50 + x = 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 + x = 0 + 50

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

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

Simplifying
x = 50
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

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

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

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {50, 10}