(x+42)*x=400

Solution for (x+42)*x=400 equation:

Simplifying
(x + 42) * x = 400

Reorder the terms:
(42 + x) * x = 400

Reorder the terms for easier multiplication:
x(42 + x) = 400
(42 * x + x * x) = 400
(42x + x2) = 400

Solving
42x + x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 42x + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 42x + x2 = 0

Factor a trinomial.
(-50 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-50 + -1x)' equal to zero and attempt to solve:

Simplifying
-50 + -1x = 0

Solving
-50 + -1x = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1x = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1x = 0 + 50
-1x = 0 + 50

Combine like terms: 0 + 50 = 50
-1x = 50

Divide each side by '-1'.
x = -50

Simplifying
x = -50
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-50, 8}