6x^2=21x-9

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

Simplifying
6x2 = 21x + -9

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

Solving
6x2 = -9 + 21x

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
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 = {0.5, 3}