(x-20)(x+6)=5760

Solution for (x-20)(x+6)=5760 equation:

Simplifying
(x + -20)(x + 6) = 5760

Reorder the terms:
(-20 + x)(x + 6) = 5760

Reorder the terms:
(-20 + x)(6 + x) = 5760

Multiply (-20 + x) * (6 + x)
(-20(6 + x) + x(6 + x)) = 5760
((6 * -20 + x * -20) + x(6 + x)) = 5760
((-120 + -20x) + x(6 + x)) = 5760
(-120 + -20x + (6 * x + x * x)) = 5760
(-120 + -20x + (6x + x2)) = 5760

Combine like terms: -20x + 6x = -14x
(-120 + -14x + x2) = 5760

Solving
-120 + -14x + x2 = 5760

Solving for variable 'x'.

Reorder the terms:
-120 + -5760 + -14x + x2 = 5760 + -5760

Combine like terms: -120 + -5760 = -5880
-5880 + -14x + x2 = 5760 + -5760

Combine like terms: 5760 + -5760 = 0
-5880 + -14x + x2 = 0

Factor a trinomial.
(-70 + -1x)(84 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(84 + -1x)' equal to zero and attempt to solve:

Simplifying
84 + -1x = 0

Solving
84 + -1x = 0

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

Add '-84' to each side of the equation.
84 + -84 + -1x = 0 + -84

Combine like terms: 84 + -84 = 0
0 + -1x = 0 + -84
-1x = 0 + -84

Combine like terms: 0 + -84 = -84
-1x = -84

Divide each side by '-1'.
x = 84

Simplifying
x = 84
Solution
x = {-70, 84}