400=x(30+x)

Solution for 400=x(30+x) equation:

Simplifying
400 = x(30 + x)
400 = (30 * x + x * x)
400 = (30x + x2)

Solving
400 = 30x + x2

Solving for variable 'x'.

Reorder the terms:
400 + -30x + -1x2 = 30x + -30x + x2 + -1x2

Combine like terms: 30x + -30x = 0
400 + -30x + -1x2 = 0 + x2 + -1x2
400 + -30x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
400 + -30x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(40 + 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 '(40 + x)' equal to zero and attempt to solve:

Simplifying
40 + x = 0

Solving
40 + x = 0

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

Add '-40' to each side of the equation.
40 + -40 + x = 0 + -40

Combine like terms: 40 + -40 = 0
0 + x = 0 + -40
x = 0 + -40

Combine like terms: 0 + -40 = -40
x = -40

Simplifying
x = -40
Solution
x = {10, -40}