x(x-20)+3(x-20)=0

Solution for x(x-20)+3(x-20)=0 equation:

Simplifying
x(x + -20) + 3(x + -20) = 0

Reorder the terms:
x(-20 + x) + 3(x + -20) = 0
(-20 * x + x * x) + 3(x + -20) = 0
(-20x + x2) + 3(x + -20) = 0

Reorder the terms:
-20x + x2 + 3(-20 + x) = 0
-20x + x2 + (-20 * 3 + x * 3) = 0
-20x + x2 + (-60 + 3x) = 0

Reorder the terms:
-60 + -20x + 3x + x2 = 0

Combine like terms: -20x + 3x = -17x
-60 + -17x + x2 = 0

Solving
-60 + -17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-3, 20}