x(x-20)=-84

Solution for x(x-20)=-84 equation:

Simplifying
x(x + -20) = -84

Reorder the terms:
x(-20 + x) = -84
(-20 * x + x * x) = -84
(-20x + x2) = -84

Solving
-20x + x2 = -84

Solving for variable 'x'.

Reorder the terms:
84 + -20x + x2 = -84 + 84

Combine like terms: -84 + 84 = 0
84 + -20x + x2 = 0

Factor a trinomial.
(6 + -1x)(14 + -1x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {6, 14}