7x=x^2-30

Solution for 7x=x^2-30 equation:

Simplifying
7x = x2 + -30

Reorder the terms:
7x = -30 + x2

Solving
7x = -30 + x2

Solving for variable 'x'.

Reorder the terms:
30 + 7x + -1x2 = -30 + x2 + 30 + -1x2

Reorder the terms:
30 + 7x + -1x2 = -30 + 30 + x2 + -1x2

Combine like terms: -30 + 30 = 0
30 + 7x + -1x2 = 0 + x2 + -1x2
30 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + 7x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {10, -3}