2x(x+2)=3(x+2)

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

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

Reorder the terms:
2x(2 + x) = 3(x + 2)
(2 * 2x + x * 2x) = 3(x + 2)
(4x + 2x2) = 3(x + 2)

Reorder the terms:
4x + 2x2 = 3(2 + x)
4x + 2x2 = (2 * 3 + x * 3)
4x + 2x2 = (6 + 3x)

Solving
4x + 2x2 = 6 + 3x

Solving for variable 'x'.

Reorder the terms:
-6 + 4x + -3x + 2x2 = 6 + 3x + -6 + -3x

Combine like terms: 4x + -3x = 1x
-6 + 1x + 2x2 = 6 + 3x + -6 + -3x

Reorder the terms:
-6 + 1x + 2x2 = 6 + -6 + 3x + -3x

Combine like terms: 6 + -6 = 0
-6 + 1x + 2x2 = 0 + 3x + -3x
-6 + 1x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6 + 1x + 2x2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-2, 1.5}