(x+20)(x-40)=2700

Solution for (x+20)(x-40)=2700 equation:

Simplifying
(x + 20)(x + -40) = 2700

Reorder the terms:
(20 + x)(x + -40) = 2700

Reorder the terms:
(20 + x)(-40 + x) = 2700

Multiply (20 + x) * (-40 + x)
(20(-40 + x) + x(-40 + x)) = 2700
((-40 * 20 + x * 20) + x(-40 + x)) = 2700
((-800 + 20x) + x(-40 + x)) = 2700
(-800 + 20x + (-40 * x + x * x)) = 2700
(-800 + 20x + (-40x + x2)) = 2700

Combine like terms: 20x + -40x = -20x
(-800 + -20x + x2) = 2700

Solving
-800 + -20x + x2 = 2700

Solving for variable 'x'.

Reorder the terms:
-800 + -2700 + -20x + x2 = 2700 + -2700

Combine like terms: -800 + -2700 = -3500
-3500 + -20x + x2 = 2700 + -2700

Combine like terms: 2700 + -2700 = 0
-3500 + -20x + x2 = 0

Factor a trinomial.
(-50 + -1x)(70 + -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 '(70 + -1x)' equal to zero and attempt to solve:

Simplifying
70 + -1x = 0

Solving
70 + -1x = 0

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

Add '-70' to each side of the equation.
70 + -70 + -1x = 0 + -70

Combine like terms: 70 + -70 = 0
0 + -1x = 0 + -70
-1x = 0 + -70

Combine like terms: 0 + -70 = -70
-1x = -70

Divide each side by '-1'.
x = 70

Simplifying
x = 70
Solution
x = {-50, 70}