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

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

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

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

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

Multiply (2 + x) * (-2 + x)
(2(-2 + x) + x(-2 + x)) + -3x = 0
((-2 * 2 + x * 2) + x(-2 + x)) + -3x = 0
((-4 + 2x) + x(-2 + x)) + -3x = 0
(-4 + 2x + (-2 * x + x * x)) + -3x = 0
(-4 + 2x + (-2x + x2)) + -3x = 0

Combine like terms: 2x + -2x = 0
(-4 + 0 + x2) + -3x = 0
(-4 + x2) + -3x = 0

Reorder the terms:
-4 + -3x + x2 = 0

Solving
-4 + -3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(4 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}