9x^2=21x-12

Solution for 9x^2=21x-12 equation:

Simplifying
9x2 = 21x + -12

Reorder the terms:
9x2 = -12 + 21x

Solving
9x2 = -12 + 21x

Solving for variable 'x'.

Reorder the terms:
12 + -21x + 9x2 = -12 + 21x + 12 + -21x

Reorder the terms:
12 + -21x + 9x2 = -12 + 12 + 21x + -21x

Combine like terms: -12 + 12 = 0
12 + -21x + 9x2 = 0 + 21x + -21x
12 + -21x + 9x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
12 + -21x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -7x + 3x2) = 0

Factor a trinomial.
3((1 + -1x)(4 + -3x)) = 0

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {1, 1.333333333}