(3x+1)(x-6)=22

Solution for (3x+1)(x-6)=22 equation:

Simplifying
(3x + 1)(x + -6) = 22

Reorder the terms:
(1 + 3x)(x + -6) = 22

Reorder the terms:
(1 + 3x)(-6 + x) = 22

Multiply (1 + 3x) * (-6 + x)
(1(-6 + x) + 3x * (-6 + x)) = 22
((-6 * 1 + x * 1) + 3x * (-6 + x)) = 22
((-6 + 1x) + 3x * (-6 + x)) = 22
(-6 + 1x + (-6 * 3x + x * 3x)) = 22
(-6 + 1x + (-18x + 3x2)) = 22

Combine like terms: 1x + -18x = -17x
(-6 + -17x + 3x2) = 22

Solving
-6 + -17x + 3x2 = 22

Solving for variable 'x'.

Reorder the terms:
-6 + -22 + -17x + 3x2 = 22 + -22

Combine like terms: -6 + -22 = -28
-28 + -17x + 3x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-28 + -17x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.333333333, 7}