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

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


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

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

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

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

Combine like terms: 1x + 6x = 7x
(2 + 7x + 3x2) = 22

Solving
2 + 7x + 3x2 = 22

Solving for variable 'x'.

Reorder the terms:
2 + -22 + 7x + 3x2 = 22 + -22

Combine like terms: 2 + -22 = -20
-20 + 7x + 3x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-20 + 7x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-4, 1.666666667}

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