4x-30=30-x^2

Solution for 4x-30=30-x^2 equation:

Simplifying
4x + -30 = 30 + -1x2

Reorder the terms:
-30 + 4x = 30 + -1x2

Solving
-30 + 4x = 30 + -1x2

Solving for variable 'x'.

Reorder the terms:
-30 + -30 + 4x + x2 = 30 + -1x2 + -30 + x2

Combine like terms: -30 + -30 = -60
-60 + 4x + x2 = 30 + -1x2 + -30 + x2

Reorder the terms:
-60 + 4x + x2 = 30 + -30 + -1x2 + x2

Combine like terms: 30 + -30 = 0
-60 + 4x + x2 = 0 + -1x2 + x2
-60 + 4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-60 + 4x + x2 = 0

Factor a trinomial.
(-10 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-10, 6}