3(x^2+8x)+2(x^2+12)=

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Solution for 3(x^2+8x)+2(x^2+12)= equation: 


Simplifying
3(x2 + 8x) + 2(x2 + 12) = 0

Reorder the terms:
3(8x + x2) + 2(x2 + 12) = 0
(8x * 3 + x2 * 3) + 2(x2 + 12) = 0
(24x + 3x2) + 2(x2 + 12) = 0

Reorder the terms:
24x + 3x2 + 2(12 + x2) = 0
24x + 3x2 + (12 * 2 + x2 * 2) = 0
24x + 3x2 + (24 + 2x2) = 0

Reorder the terms:
24 + 24x + 3x2 + 2x2 = 0

Combine like terms: 3x2 + 2x2 = 5x2
24 + 24x + 5x2 = 0

Solving
24 + 24x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
4.8 + 4.8x + x2 = 0

Move the constant term to the right:

Add '-4.8' to each side of the equation.
4.8 + 4.8x + -4.8 + x2 = 0 + -4.8

Reorder the terms:
4.8 + -4.8 + 4.8x + x2 = 0 + -4.8

Combine like terms: 4.8 + -4.8 = 0.0
0.0 + 4.8x + x2 = 0 + -4.8
4.8x + x2 = 0 + -4.8

Combine like terms: 0 + -4.8 = -4.8
4.8x + x2 = -4.8

The x term is 4.8x.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8x + 5.76 + x2 = -4.8 + 5.76

Reorder the terms:
5.76 + 4.8x + x2 = -4.8 + 5.76

Combine like terms: -4.8 + 5.76 = 0.96
5.76 + 4.8x + x2 = 0.96

Factor a perfect square on the left side:
(x + 2.4)(x + 2.4) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(x + 2.4) equal to 0.979795897 and -0.979795897.


Subproblem 1
x + 2.4 = 0.979795897

Simplifying
x + 2.4 = 0.979795897

Reorder the terms:
2.4 + x = 0.979795897

Solving
2.4 + x = 0.979795897

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = 0.979795897 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = 0.979795897 + -2.4
x = 0.979795897 + -2.4

Combine like terms: 0.979795897 + -2.4 = -1.420204103
x = -1.420204103

Simplifying
x = -1.420204103


Subproblem 2
x + 2.4 = -0.979795897

Simplifying
x + 2.4 = -0.979795897

Reorder the terms:
2.4 + x = -0.979795897

Solving
2.4 + x = -0.979795897

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = -0.979795897 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = -0.979795897 + -2.4
x = -0.979795897 + -2.4

Combine like terms: -0.979795897 + -2.4 = -3.379795897
x = -3.379795897

Simplifying
x = -3.379795897


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.420204103, -3.379795897}

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