3x(x-2)=11x+6

Solution for 3x(x-2)=11x+6 equation:

Simplifying
3x(x + -2) = 11x + 6

Reorder the terms:
3x(-2 + x) = 11x + 6
(-2 * 3x + x * 3x) = 11x + 6
(-6x + 3x2) = 11x + 6

Reorder the terms:
-6x + 3x2 = 6 + 11x

Solving
-6x + 3x2 = 6 + 11x

Solving for variable 'x'.

Reorder the terms:
-6 + -6x + -11x + 3x2 = 6 + 11x + -6 + -11x

Combine like terms: -6x + -11x = -17x
-6 + -17x + 3x2 = 6 + 11x + -6 + -11x

Reorder the terms:
-6 + -17x + 3x2 = 6 + -6 + 11x + -11x

Combine like terms: 6 + -6 = 0
-6 + -17x + 3x2 = 0 + 11x + -11x
-6 + -17x + 3x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-6 + -17x + 3x2 = 0

Factor a trinomial.
(-1 + -3x)(6 + -1x) = 0

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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-0.3333333333, 6}