(3x-1)(x+2)=x^2-4

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Solution for (3x-1)(x+2)=x^2-4 equation: 


Simplifying
(3x + -1)(x + 2) = x2 + -4

Reorder the terms:
(-1 + 3x)(x + 2) = x2 + -4

Reorder the terms:
(-1 + 3x)(2 + x) = x2 + -4

Multiply (-1 + 3x) * (2 + x)
(-1(2 + x) + 3x * (2 + x)) = x2 + -4
((2 * -1 + x * -1) + 3x * (2 + x)) = x2 + -4
((-2 + -1x) + 3x * (2 + x)) = x2 + -4
(-2 + -1x + (2 * 3x + x * 3x)) = x2 + -4
(-2 + -1x + (6x + 3x2)) = x2 + -4

Combine like terms: -1x + 6x = 5x
(-2 + 5x + 3x2) = x2 + -4

Reorder the terms:
-2 + 5x + 3x2 = -4 + x2

Solving
-2 + 5x + 3x2 = -4 + x2

Solving for variable 'x'.

Reorder the terms:
-2 + 4 + 5x + 3x2 + -1x2 = -4 + x2 + 4 + -1x2

Combine like terms: -2 + 4 = 2
2 + 5x + 3x2 + -1x2 = -4 + x2 + 4 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
2 + 5x + 2x2 = -4 + x2 + 4 + -1x2

Reorder the terms:
2 + 5x + 2x2 = -4 + 4 + x2 + -1x2

Combine like terms: -4 + 4 = 0
2 + 5x + 2x2 = 0 + x2 + -1x2
2 + 5x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 5x + 2x2 = 0

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


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

Simplifying
2 + x = 0

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

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

Combine like terms: 0 + -2 = -2
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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