30-(x^2)+x=10

Solution for 30-(x^2)+x=10 equation:

Simplifying
30 + -1(x2) + x = 10

Reorder the terms:
30 + x + -1x2 = 10

Solving
30 + x + -1x2 = 10

Solving for variable 'x'.

Reorder the terms:
30 + -10 + x + -1x2 = 10 + -10

Combine like terms: 30 + -10 = 20
20 + x + -1x2 = 10 + -10

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

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

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

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