(3x+2)(x+1)=(2x-1)(x+6)

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Solution for (3x+2)(x+1)=(2x-1)(x+6) equation: 


Simplifying
(3x + 2)(x + 1) = (2x + -1)(x + 6)

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

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

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

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

Reorder the terms:
2 + 5x + 3x2 = (-1 + 2x)(x + 6)

Reorder the terms:
2 + 5x + 3x2 = (-1 + 2x)(6 + x)

Multiply (-1 + 2x) * (6 + x)
2 + 5x + 3x2 = (-1(6 + x) + 2x * (6 + x))
2 + 5x + 3x2 = ((6 * -1 + x * -1) + 2x * (6 + x))
2 + 5x + 3x2 = ((-6 + -1x) + 2x * (6 + x))
2 + 5x + 3x2 = (-6 + -1x + (6 * 2x + x * 2x))
2 + 5x + 3x2 = (-6 + -1x + (12x + 2x2))

Combine like terms: -1x + 12x = 11x
2 + 5x + 3x2 = (-6 + 11x + 2x2)

Solving
2 + 5x + 3x2 = -6 + 11x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + 6 + 5x + -11x + 3x2 + -2x2 = -6 + 11x + 2x2 + 6 + -11x + -2x2

Combine like terms: 2 + 6 = 8
8 + 5x + -11x + 3x2 + -2x2 = -6 + 11x + 2x2 + 6 + -11x + -2x2

Combine like terms: 5x + -11x = -6x
8 + -6x + 3x2 + -2x2 = -6 + 11x + 2x2 + 6 + -11x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
8 + -6x + 1x2 = -6 + 11x + 2x2 + 6 + -11x + -2x2

Reorder the terms:
8 + -6x + 1x2 = -6 + 6 + 11x + -11x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
8 + -6x + 1x2 = 0 + 11x + -11x + 2x2 + -2x2
8 + -6x + 1x2 = 11x + -11x + 2x2 + -2x2

Combine like terms: 11x + -11x = 0
8 + -6x + 1x2 = 0 + 2x2 + -2x2
8 + -6x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + -6x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}

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