6(3x^2+8x+4)=0

Solution for 6(3x^2+8x+4)=0 equation:

Simplifying
6(3x2 + 8x + 4) = 0

Reorder the terms:
6(4 + 8x + 3x2) = 0
(4 * 6 + 8x * 6 + 3x2 * 6) = 0
(24 + 48x + 18x2) = 0

Solving
24 + 48x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + 8x + 3x2) = 0

Factor a trinomial.
6((2 + x)(2 + 3x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-2, -0.6666666667}