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

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

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

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

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

Multiply (3 + 2x) * (-2 + x)
2(3(-2 + x) + 2x * (-2 + x)) = 0
2((-2 * 3 + x * 3) + 2x * (-2 + x)) = 0
2((-6 + 3x) + 2x * (-2 + x)) = 0
2(-6 + 3x + (-2 * 2x + x * 2x)) = 0
2(-6 + 3x + (-4x + 2x2)) = 0

Combine like terms: 3x + -4x = -1x
2(-6 + -1x + 2x2) = 0
(-6 * 2 + -1x * 2 + 2x2 * 2) = 0
(-12 + -2x + 4x2) = 0

Solving
-12 + -2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1x + 2x2) = 0

Factor a trinomial.
2((-3 + -2x)(2 + -1x)) = 0

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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.5, 2}