0=(x+4)(x-42)

Solution for 0=(x+4)(x-42) equation:

Simplifying
0 = (x + 4)(x + -42)

Reorder the terms:
0 = (4 + x)(x + -42)

Reorder the terms:
0 = (4 + x)(-42 + x)

Multiply (4 + x) * (-42 + x)
0 = (4(-42 + x) + x(-42 + x))
0 = ((-42 * 4 + x * 4) + x(-42 + x))
0 = ((-168 + 4x) + x(-42 + x))
0 = (-168 + 4x + (-42 * x + x * x))
0 = (-168 + 4x + (-42x + x2))

Combine like terms: 4x + -42x = -38x
0 = (-168 + -38x + x2)

Solving
0 = -168 + -38x + x2

Solving for variable 'x'.

Combine like terms: 0 + 168 = 168
168 + 38x + -1x2 = -168 + -38x + x2 + 168 + 38x + -1x2

Reorder the terms:
168 + 38x + -1x2 = -168 + 168 + -38x + 38x + x2 + -1x2

Combine like terms: -168 + 168 = 0
168 + 38x + -1x2 = 0 + -38x + 38x + x2 + -1x2
168 + 38x + -1x2 = -38x + 38x + x2 + -1x2

Combine like terms: -38x + 38x = 0
168 + 38x + -1x2 = 0 + x2 + -1x2
168 + 38x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
168 + 38x + -1x2 = 0

Factor a trinomial.
(42 + -1x)(4 + x) = 0

Subproblem 1
Set the factor '(42 + -1x)' equal to zero and attempt to solve:

Simplifying
42 + -1x = 0

Solving
42 + -1x = 0

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

Add '-42' to each side of the equation.
42 + -42 + -1x = 0 + -42

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

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

Divide each side by '-1'.
x = 42

Simplifying
x = 42
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {42, -4}