0=6x^2-11x-21

Solution for 0=6x^2-11x-21 equation:

Simplifying
0 = 6x2 + -11x + -21

Reorder the terms:
0 = -21 + -11x + 6x2

Solving
0 = -21 + -11x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 21 = 21
21 + 11x + -6x2 = -21 + -11x + 6x2 + 21 + 11x + -6x2

Reorder the terms:
21 + 11x + -6x2 = -21 + 21 + -11x + 11x + 6x2 + -6x2

Combine like terms: -21 + 21 = 0
21 + 11x + -6x2 = 0 + -11x + 11x + 6x2 + -6x2
21 + 11x + -6x2 = -11x + 11x + 6x2 + -6x2

Combine like terms: -11x + 11x = 0
21 + 11x + -6x2 = 0 + 6x2 + -6x2
21 + 11x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
21 + 11x + -6x2 = 0

Factor a trinomial.
(3 + -1x)(7 + 6x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {3, -1.166666667}