(3x-1)(x+2)=(2x-1)(x+3)+5

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Solution for (3x-1)(x+2)=(2x-1)(x+3)+5 equation: 


Simplifying
(3x + -1)(x + 2) = (2x + -1)(x + 3) + 5

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

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

Multiply (-1 + 3x) * (2 + x)
(-1(2 + x) + 3x * (2 + x)) = (2x + -1)(x + 3) + 5
((2 * -1 + x * -1) + 3x * (2 + x)) = (2x + -1)(x + 3) + 5
((-2 + -1x) + 3x * (2 + x)) = (2x + -1)(x + 3) + 5
(-2 + -1x + (2 * 3x + x * 3x)) = (2x + -1)(x + 3) + 5
(-2 + -1x + (6x + 3x2)) = (2x + -1)(x + 3) + 5

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

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

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

Multiply (-1 + 2x) * (3 + x)
-2 + 5x + 3x2 = (-1(3 + x) + 2x * (3 + x)) + 5
-2 + 5x + 3x2 = ((3 * -1 + x * -1) + 2x * (3 + x)) + 5
-2 + 5x + 3x2 = ((-3 + -1x) + 2x * (3 + x)) + 5
-2 + 5x + 3x2 = (-3 + -1x + (3 * 2x + x * 2x)) + 5
-2 + 5x + 3x2 = (-3 + -1x + (6x + 2x2)) + 5

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

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

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

Add '-5x' to each side of the equation.
-2 + 5x + -5x + 3x2 = 2 + 5x + -5x + 2x2

Combine like terms: 5x + -5x = 0
-2 + 0 + 3x2 = 2 + 5x + -5x + 2x2
-2 + 3x2 = 2 + 5x + -5x + 2x2

Combine like terms: 5x + -5x = 0
-2 + 3x2 = 2 + 0 + 2x2
-2 + 3x2 = 2 + 2x2

Solving
-2 + 3x2 = 2 + 2x2

Solving for variable 'x'.

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

Add '-2x2' to each side of the equation.
-2 + 3x2 + -2x2 = 2 + 2x2 + -2x2

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

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

Add '2' to each side of the equation.
-2 + 2 + 1x2 = 2 + 2

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

Combine like terms: 2 + 2 = 4
1x2 = 4

Divide each side by '1'.
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}

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