(30+x)(x)=400

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

Simplifying
(30 + x)(x) = 400

Reorder the terms for easier multiplication:
x(30 + x) = 400
(30 * x + x * x) = 400
(30x + x2) = 400

Solving
30x + x2 = 400

Solving for variable 'x'.

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

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

Factor a trinomial.
(-40 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-40 + -1x)' equal to zero and attempt to solve:

Simplifying
-40 + -1x = 0

Solving
-40 + -1x = 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 + -1x = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -1x = 0 + 40
-1x = 0 + 40

Combine like terms: 0 + 40 = 40
-1x = 40

Divide each side by '-1'.
x = -40

Simplifying
x = -40
Subproblem 2
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
Solution
x = {-40, 10}