-6x=3x^2+3

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

Simplifying
-6x = 3x2 + 3

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

Solving
-6x = 3 + 3x2

Solving for variable 'x'.

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

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

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

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

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

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

Ignore the factor -3.
Subproblem 1
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
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 = {-1, -1}