0=x^2+42x-400

Solution for 0=x^2+42x-400 equation:

Simplifying
0 = x2 + 42x + -400

Reorder the terms:
0 = -400 + 42x + x2

Solving
0 = -400 + 42x + x2

Solving for variable 'x'.

Combine like terms: 0 + 400 = 400
400 + -42x + -1x2 = -400 + 42x + x2 + 400 + -42x + -1x2

Reorder the terms:
400 + -42x + -1x2 = -400 + 400 + 42x + -42x + x2 + -1x2

Combine like terms: -400 + 400 = 0
400 + -42x + -1x2 = 0 + 42x + -42x + x2 + -1x2
400 + -42x + -1x2 = 42x + -42x + x2 + -1x2

Combine like terms: 42x + -42x = 0
400 + -42x + -1x2 = 0 + x2 + -1x2
400 + -42x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
400 + -42x + -1x2 = 0

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

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

Simplifying
50 + x = 0

Solving
50 + x = 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 + x = 0 + -50

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

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

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