3*x^2=(6*x)+9

Solution for 3*x^2=(6*x)+9 equation:

Simplifying
3x2 = (6x) + 9

Reorder the terms:
3x2 = 9 + (6x)

Solving
3x2 = 9 + (6x)

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
3((-1 + -1x)(3 + -1x)) = 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 '(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 = {-1, 3}