6x-3x^2=-9

Solution for 6x-3x^2=-9 equation:

Simplifying
6x + -3x2 = -9

Solving
6x + -3x2 = -9

Solving for variable 'x'.

Reorder the terms:
9 + 6x + -3x2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + 6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 2x + -1x2) = 0

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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {3, -1}