(3x+2)(x-1)=x(x+2)

Solution for (3x+2)(x-1)=x(x+2) equation:

Simplifying
(3x + 2)(x + -1) = x(x + 2)

Reorder the terms:
(2 + 3x)(x + -1) = x(x + 2)

Reorder the terms:
(2 + 3x)(-1 + x) = x(x + 2)

Multiply (2 + 3x) * (-1 + x)
(2(-1 + x) + 3x * (-1 + x)) = x(x + 2)
((-1 * 2 + x * 2) + 3x * (-1 + x)) = x(x + 2)
((-2 + 2x) + 3x * (-1 + x)) = x(x + 2)
(-2 + 2x + (-1 * 3x + x * 3x)) = x(x + 2)
(-2 + 2x + (-3x + 3x2)) = x(x + 2)

Combine like terms: 2x + -3x = -1x
(-2 + -1x + 3x2) = x(x + 2)

Reorder the terms:
-2 + -1x + 3x2 = x(2 + x)
-2 + -1x + 3x2 = (2 * x + x * x)
-2 + -1x + 3x2 = (2x + x2)

Solving
-2 + -1x + 3x2 = 2x + x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
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 = {-0.5, 2}