9x^2=21x-6

Solution for 9x^2=21x-6 equation:

Simplifying
9x2 = 21x + -6

Reorder the terms:
9x2 = -6 + 21x

Solving
9x2 = -6 + 21x

Solving for variable 'x'.

Reorder the terms:
6 + -21x + 9x2 = -6 + 21x + 6 + -21x

Reorder the terms:
6 + -21x + 9x2 = -6 + 6 + 21x + -21x

Combine like terms: -6 + 6 = 0
6 + -21x + 9x2 = 0 + 21x + -21x
6 + -21x + 9x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
6 + -21x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -7x + 3x2) = 0

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.3333333333, 2}