3x^2=11x-6

Solution for 3x^2=11x-6 equation:

Simplifying
3x2 = 11x + -6

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

Solving
3x2 = -6 + 11x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(2 + -3x)(3 + -1x) = 0

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.6666666667, 3}