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

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


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

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

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

Multiply (-1 + 3x) * (2 + x)
(-1(2 + x) + 3x * (2 + x)) = x(x + 2)
((2 * -1 + x * -1) + 3x * (2 + x)) = x(x + 2)
((-2 + -1x) + 3x * (2 + x)) = x(x + 2)
(-2 + -1x + (2 * 3x + x * 3x)) = x(x + 2)
(-2 + -1x + (6x + 3x2)) = x(x + 2)

Combine like terms: -1x + 6x = 5x
(-2 + 5x + 3x2) = x(x + 2)

Reorder the terms:
-2 + 5x + 3x2 = x(2 + x)
-2 + 5x + 3x2 = (2 * x + x * x)
-2 + 5x + 3x2 = (2x + x2)

Solving
-2 + 5x + 3x2 = 2x + x2

Solving for variable 'x'.

Reorder the terms:
-2 + 5x + -2x + 3x2 + -1x2 = 2x + x2 + -2x + -1x2

Combine like terms: 5x + -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.
(-2 + -1x)(1 + -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 '(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
Solution
x = {-2, 0.5}

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