22=(3x+1)(2x+1)

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Solution for 22=(3x+1)(2x+1) equation: 


Simplifying
22 = (3x + 1)(2x + 1)

Reorder the terms:
22 = (1 + 3x)(2x + 1)

Reorder the terms:
22 = (1 + 3x)(1 + 2x)

Multiply (1 + 3x) * (1 + 2x)
22 = (1(1 + 2x) + 3x * (1 + 2x))
22 = ((1 * 1 + 2x * 1) + 3x * (1 + 2x))
22 = ((1 + 2x) + 3x * (1 + 2x))
22 = (1 + 2x + (1 * 3x + 2x * 3x))
22 = (1 + 2x + (3x + 6x2))

Combine like terms: 2x + 3x = 5x
22 = (1 + 5x + 6x2)

Solving
22 = 1 + 5x + 6x2

Solving for variable 'x'.

Combine like terms: 22 + -1 = 21
21 + -5x + -6x2 = 1 + 5x + 6x2 + -1 + -5x + -6x2

Reorder the terms:
21 + -5x + -6x2 = 1 + -1 + 5x + -5x + 6x2 + -6x2

Combine like terms: 1 + -1 = 0
21 + -5x + -6x2 = 0 + 5x + -5x + 6x2 + -6x2
21 + -5x + -6x2 = 5x + -5x + 6x2 + -6x2

Combine like terms: 5x + -5x = 0
21 + -5x + -6x2 = 0 + 6x2 + -6x2
21 + -5x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
21 + -5x + -6x2 = 0

Factor a trinomial.
(3 + -2x)(7 + 3x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {1.5, -2.333333333}

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