(2x+1)(3x-1)=6

Solution for (2x+1)(3x-1)=6 equation:

Simplifying
(2x + 1)(3x + -1) = 6

Reorder the terms:
(1 + 2x)(3x + -1) = 6

Reorder the terms:
(1 + 2x)(-1 + 3x) = 6

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

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

Solving
-1 + 1x + 6x2 = 6

Solving for variable 'x'.

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

Combine like terms: -1 + -6 = -7
-7 + 1x + 6x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-7 + 1x + 6x2 = 0

Factor a trinomial.
(-7 + -6x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -6x)' equal to zero and attempt to solve:

Simplifying
-7 + -6x = 0

Solving
-7 + -6x = 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 + -6x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6x = 0 + 7
-6x = 0 + 7

Combine like terms: 0 + 7 = 7
-6x = 7

Divide each side by '-6'.
x = -1.166666667

Simplifying
x = -1.166666667
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 = {-1.166666667, 1}