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

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


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

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

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

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

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

Solving
1 + 5x + 6x2 = 22

Solving for variable 'x'.

Reorder the terms:
1 + -22 + 5x + 6x2 = 22 + -22

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

Combine like terms: 22 + -22 = 0
-21 + 5x + 6x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-2.333333333, 1.5}

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