x(x+2)+3(x-2)=0

Solution for x(x+2)+3(x-2)=0 equation:

Simplifying
x(x + 2) + 3(x + -2) = 0

Reorder the terms:
x(2 + x) + 3(x + -2) = 0
(2 * x + x * x) + 3(x + -2) = 0
(2x + x2) + 3(x + -2) = 0

Reorder the terms:
2x + x2 + 3(-2 + x) = 0
2x + x2 + (-2 * 3 + x * 3) = 0
2x + x2 + (-6 + 3x) = 0

Reorder the terms:
-6 + 2x + 3x + x2 = 0

Combine like terms: 2x + 3x = 5x
-6 + 5x + x2 = 0

Solving
-6 + 5x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-6, 1}