(2x-1)(3x+1)=11

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Solution for (2x-1)(3x+1)=11 equation: 


Simplifying
(2x + -1)(3x + 1) = 11

Reorder the terms:
(-1 + 2x)(3x + 1) = 11

Reorder the terms:
(-1 + 2x)(1 + 3x) = 11

Multiply (-1 + 2x) * (1 + 3x)
(-1(1 + 3x) + 2x * (1 + 3x)) = 11
((1 * -1 + 3x * -1) + 2x * (1 + 3x)) = 11
((-1 + -3x) + 2x * (1 + 3x)) = 11
(-1 + -3x + (1 * 2x + 3x * 2x)) = 11
(-1 + -3x + (2x + 6x2)) = 11

Combine like terms: -3x + 2x = -1x
(-1 + -1x + 6x2) = 11

Solving
-1 + -1x + 6x2 = 11

Solving for variable 'x'.

Reorder the terms:
-1 + -11 + -1x + 6x2 = 11 + -11

Combine like terms: -1 + -11 = -12
-12 + -1x + 6x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-12 + -1x + 6x2 = 0

Factor a trinomial.
(-4 + -3x)(3 + -2x) = 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 '(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 = {-1.333333333, 1.5}

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