(2x+1)(x+3)-9=(3x-2)(x+2)

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Solution for (2x+1)(x+3)-9=(3x-2)(x+2) equation: 


Simplifying
(2x + 1)(x + 3) + -9 = (3x + -2)(x + 2)

Reorder the terms:
(1 + 2x)(x + 3) + -9 = (3x + -2)(x + 2)

Reorder the terms:
(1 + 2x)(3 + x) + -9 = (3x + -2)(x + 2)

Multiply (1 + 2x) * (3 + x)
(1(3 + x) + 2x * (3 + x)) + -9 = (3x + -2)(x + 2)
((3 * 1 + x * 1) + 2x * (3 + x)) + -9 = (3x + -2)(x + 2)
((3 + 1x) + 2x * (3 + x)) + -9 = (3x + -2)(x + 2)
(3 + 1x + (3 * 2x + x * 2x)) + -9 = (3x + -2)(x + 2)
(3 + 1x + (6x + 2x2)) + -9 = (3x + -2)(x + 2)

Combine like terms: 1x + 6x = 7x
(3 + 7x + 2x2) + -9 = (3x + -2)(x + 2)

Reorder the terms:
3 + -9 + 7x + 2x2 = (3x + -2)(x + 2)

Combine like terms: 3 + -9 = -6
-6 + 7x + 2x2 = (3x + -2)(x + 2)

Reorder the terms:
-6 + 7x + 2x2 = (-2 + 3x)(x + 2)

Reorder the terms:
-6 + 7x + 2x2 = (-2 + 3x)(2 + x)

Multiply (-2 + 3x) * (2 + x)
-6 + 7x + 2x2 = (-2(2 + x) + 3x * (2 + x))
-6 + 7x + 2x2 = ((2 * -2 + x * -2) + 3x * (2 + x))
-6 + 7x + 2x2 = ((-4 + -2x) + 3x * (2 + x))
-6 + 7x + 2x2 = (-4 + -2x + (2 * 3x + x * 3x))
-6 + 7x + 2x2 = (-4 + -2x + (6x + 3x2))

Combine like terms: -2x + 6x = 4x
-6 + 7x + 2x2 = (-4 + 4x + 3x2)

Solving
-6 + 7x + 2x2 = -4 + 4x + 3x2

Solving for variable 'x'.

Reorder the terms:
-6 + 4 + 7x + -4x + 2x2 + -3x2 = -4 + 4x + 3x2 + 4 + -4x + -3x2

Combine like terms: -6 + 4 = -2
-2 + 7x + -4x + 2x2 + -3x2 = -4 + 4x + 3x2 + 4 + -4x + -3x2

Combine like terms: 7x + -4x = 3x
-2 + 3x + 2x2 + -3x2 = -4 + 4x + 3x2 + 4 + -4x + -3x2

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

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

Combine like terms: -4 + 4 = 0
-2 + 3x + -1x2 = 0 + 4x + -4x + 3x2 + -3x2
-2 + 3x + -1x2 = 4x + -4x + 3x2 + -3x2

Combine like terms: 4x + -4x = 0
-2 + 3x + -1x2 = 0 + 3x2 + -3x2
-2 + 3x + -1x2 = 3x2 + -3x2

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {2, 1}

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