0=3x^2+24x+43

Solution for 0=3x^2+24x+43 equation:

Simplifying
0 = 3x2 + 24x + 43

Reorder the terms:
0 = 43 + 24x + 3x2

Solving
0 = 43 + 24x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -43 = -43
-43 + -24x + -3x2 = 43 + 24x + 3x2 + -43 + -24x + -3x2

Reorder the terms:
-43 + -24x + -3x2 = 43 + -43 + 24x + -24x + 3x2 + -3x2

Combine like terms: 43 + -43 = 0
-43 + -24x + -3x2 = 0 + 24x + -24x + 3x2 + -3x2
-43 + -24x + -3x2 = 24x + -24x + 3x2 + -3x2

Combine like terms: 24x + -24x = 0
-43 + -24x + -3x2 = 0 + 3x2 + -3x2
-43 + -24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-43 + -24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(43 + 24x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(43 + 24x + 3x2)' equal to zero and attempt to solve:

Simplifying
43 + 24x + 3x2 = 0

Solving
43 + 24x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
14.33333333 + 8x + x2 = 0

Move the constant term to the right:

Add '-14.33333333' to each side of the equation.
14.33333333 + 8x + -14.33333333 + x2 = 0 + -14.33333333

Reorder the terms:
14.33333333 + -14.33333333 + 8x + x2 = 0 + -14.33333333

Combine like terms: 14.33333333 + -14.33333333 = 0.00000000
0.00000000 + 8x + x2 = 0 + -14.33333333
8x + x2 = 0 + -14.33333333

Combine like terms: 0 + -14.33333333 = -14.33333333
8x + x2 = -14.33333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -14.33333333 + 16

Reorder the terms:
16 + 8x + x2 = -14.33333333 + 16

Combine like terms: -14.33333333 + 16 = 1.66666667
16 + 8x + x2 = 1.66666667

Factor a perfect square on the left side:
(x + 4)(x + 4) = 1.66666667

Calculate the square root of the right side: 1.29099445

Break this problem into two subproblems by setting 
(x + 4) equal to 1.29099445 and -1.29099445.

Subproblem 1
x + 4 = 1.29099445

Simplifying
x + 4 = 1.29099445

Reorder the terms:
4 + x = 1.29099445

Solving
4 + x = 1.29099445

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 1.29099445 + -4

Combine like terms: 4 + -4 = 0
0 + x = 1.29099445 + -4
x = 1.29099445 + -4

Combine like terms: 1.29099445 + -4 = -2.70900555
x = -2.70900555

Simplifying
x = -2.70900555

Subproblem 2
x + 4 = -1.29099445

Simplifying
x + 4 = -1.29099445

Reorder the terms:
4 + x = -1.29099445

Solving
4 + x = -1.29099445

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -1.29099445 + -4

Combine like terms: 4 + -4 = 0
0 + x = -1.29099445 + -4
x = -1.29099445 + -4

Combine like terms: -1.29099445 + -4 = -5.29099445
x = -5.29099445

Simplifying
x = -5.29099445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.70900555, -5.29099445}
Solution
x = {-2.70900555, -5.29099445}