2(3x-6)+(3x^2-4+7)=0

Solution for 2(3x-6)+(3x^2-4+7)=0 equation:

Simplifying
2(3x + -6) + (3x2 + -4 + 7) = 0

Reorder the terms:
2(-6 + 3x) + (3x2 + -4 + 7) = 0
(-6 * 2 + 3x * 2) + (3x2 + -4 + 7) = 0
(-12 + 6x) + (3x2 + -4 + 7) = 0

Reorder the terms:
-12 + 6x + (-4 + 7 + 3x2) = 0

Combine like terms: -4 + 7 = 3
-12 + 6x + (3 + 3x2) = 0

Remove parenthesis around (3 + 3x2)
-12 + 6x + 3 + 3x2 = 0

Reorder the terms:
-12 + 3 + 6x + 3x2 = 0

Combine like terms: -12 + 3 = -9
-9 + 6x + 3x2 = 0

Solving
-9 + 6x + 3x2 = 0

Solving for variable 'x'.

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

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