10x+300=900-x^2

Solution for 10x+300=900-x^2 equation:

Simplifying
10x + 300 = 900 + -1x2

Reorder the terms:
300 + 10x = 900 + -1x2

Solving
300 + 10x = 900 + -1x2

Solving for variable 'x'.

Reorder the terms:
300 + -900 + 10x + x2 = 900 + -1x2 + -900 + x2

Combine like terms: 300 + -900 = -600
-600 + 10x + x2 = 900 + -1x2 + -900 + x2

Reorder the terms:
-600 + 10x + x2 = 900 + -900 + -1x2 + x2

Combine like terms: 900 + -900 = 0
-600 + 10x + x2 = 0 + -1x2 + x2
-600 + 10x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-600 + 10x + x2 = 0

Factor a trinomial.
(-30 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(-30 + -1x)' equal to zero and attempt to solve:

Simplifying
-30 + -1x = 0

Solving
-30 + -1x = 0

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

Add '30' to each side of the equation.
-30 + 30 + -1x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1x = 0 + 30
-1x = 0 + 30

Combine like terms: 0 + 30 = 30
-1x = 30

Divide each side by '-1'.
x = -30

Simplifying
x = -30
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

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

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

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-30, 20}