5+2(12+4x)3x=

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Solution for 5+2(12+4x)3x= equation: 


Simplifying
5 + 2(12 + 4x) * 3x = 0

Reorder the terms for easier multiplication:
5 + 2 * 3x(12 + 4x) = 0

Multiply 2 * 3
5 + 6x(12 + 4x) = 0
5 + (12 * 6x + 4x * 6x) = 0
5 + (72x + 24x2) = 0

Solving
5 + 72x + 24x2 = 0

Solving for variable 'x'.

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

Divide each side by '24'.
0.2083333333 + 3x + x2 = 0

Move the constant term to the right:

Add '-0.2083333333' to each side of the equation.
0.2083333333 + 3x + -0.2083333333 + x2 = 0 + -0.2083333333

Reorder the terms:
0.2083333333 + -0.2083333333 + 3x + x2 = 0 + -0.2083333333

Combine like terms: 0.2083333333 + -0.2083333333 = 0.0000000000
0.0000000000 + 3x + x2 = 0 + -0.2083333333
3x + x2 = 0 + -0.2083333333

Combine like terms: 0 + -0.2083333333 = -0.2083333333
3x + x2 = -0.2083333333

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -0.2083333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -0.2083333333 + 2.25

Combine like terms: -0.2083333333 + 2.25 = 2.0416666667
2.25 + 3x + x2 = 2.0416666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.0416666667

Calculate the square root of the right side: 1.428869017

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.428869017 and -1.428869017.


Subproblem 1
x + 1.5 = 1.428869017

Simplifying
x + 1.5 = 1.428869017

Reorder the terms:
1.5 + x = 1.428869017

Solving
1.5 + x = 1.428869017

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.428869017 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.428869017 + -1.5
x = 1.428869017 + -1.5

Combine like terms: 1.428869017 + -1.5 = -0.071130983
x = -0.071130983

Simplifying
x = -0.071130983


Subproblem 2
x + 1.5 = -1.428869017

Simplifying
x + 1.5 = -1.428869017

Reorder the terms:
1.5 + x = -1.428869017

Solving
1.5 + x = -1.428869017

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.428869017 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.428869017 + -1.5
x = -1.428869017 + -1.5

Combine like terms: -1.428869017 + -1.5 = -2.928869017
x = -2.928869017

Simplifying
x = -2.928869017


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.071130983, -2.928869017}

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