(x-80)(x+5)=0

Solution for (x-80)(x+5)=0 equation:

Simplifying
(x + -80)(x + 5) = 0

Reorder the terms:
(-80 + x)(x + 5) = 0

Reorder the terms:
(-80 + x)(5 + x) = 0

Multiply (-80 + x) * (5 + x)
(-80(5 + x) + x(5 + x)) = 0
((5 * -80 + x * -80) + x(5 + x)) = 0
((-400 + -80x) + x(5 + x)) = 0
(-400 + -80x + (5 * x + x * x)) = 0
(-400 + -80x + (5x + x2)) = 0

Combine like terms: -80x + 5x = -75x
(-400 + -75x + x2) = 0

Solving
-400 + -75x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(80 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(80 + -1x)' equal to zero and attempt to solve:

Simplifying
80 + -1x = 0

Solving
80 + -1x = 0

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

Add '-80' to each side of the equation.
80 + -80 + -1x = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -1x = 0 + -80
-1x = 0 + -80

Combine like terms: 0 + -80 = -80
-1x = -80

Divide each side by '-1'.
x = 80

Simplifying
x = 80
Solution
x = {-5, 80}