(x-4)(x+39)=0

Solution for (x-4)(x+39)=0 equation:

Simplifying
(x + -4)(x + 39) = 0

Reorder the terms:
(-4 + x)(x + 39) = 0

Reorder the terms:
(-4 + x)(39 + x) = 0

Multiply (-4 + x) * (39 + x)
(-4(39 + x) + x(39 + x)) = 0
((39 * -4 + x * -4) + x(39 + x)) = 0
((-156 + -4x) + x(39 + x)) = 0
(-156 + -4x + (39 * x + x * x)) = 0
(-156 + -4x + (39x + x2)) = 0

Combine like terms: -4x + 39x = 35x
(-156 + 35x + x2) = 0

Solving
-156 + 35x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-39 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-39 + -1x)' equal to zero and attempt to solve:

Simplifying
-39 + -1x = 0

Solving
-39 + -1x = 0

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

Add '39' to each side of the equation.
-39 + 39 + -1x = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -1x = 0 + 39
-1x = 0 + 39

Combine like terms: 0 + 39 = 39
-1x = 39

Divide each side by '-1'.
x = -39

Simplifying
x = -39
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-39, 4}