8x(4x+12)=20

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Solution for 8x(4x+12)=20 equation: 


Simplifying
8x(4x + 12) = 20

Reorder the terms:
8x(12 + 4x) = 20
(12 * 8x + 4x * 8x) = 20
(96x + 32x2) = 20

Solving
96x + 32x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 96x + 32x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 96x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 24x + 8x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + 24x + 8x2)' equal to zero and attempt to solve:

Simplifying
-5 + 24x + 8x2 = 0

Solving
-5 + 24x + 8x2 = 0

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

Divide each side by '8'.
-0.625 + 3x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 3x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 3x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 3x + x2 = 0 + 0.625
3x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
3x + x2 = 0.625

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 = 0.625 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.625 + 2.25

Combine like terms: 0.625 + 2.25 = 2.875
2.25 + 3x + x2 = 2.875

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.875

Calculate the square root of the right side: 1.695582496

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.695582496 and -1.695582496.


Subproblem 1
x + 1.5 = 1.695582496

Simplifying
x + 1.5 = 1.695582496

Reorder the terms:
1.5 + x = 1.695582496

Solving
1.5 + x = 1.695582496

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 = 1.695582496 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.695582496 + -1.5
x = 1.695582496 + -1.5

Combine like terms: 1.695582496 + -1.5 = 0.195582496
x = 0.195582496

Simplifying
x = 0.195582496


Subproblem 2
x + 1.5 = -1.695582496

Simplifying
x + 1.5 = -1.695582496

Reorder the terms:
1.5 + x = -1.695582496

Solving
1.5 + x = -1.695582496

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 = -1.695582496 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.695582496 + -1.5
x = -1.695582496 + -1.5

Combine like terms: -1.695582496 + -1.5 = -3.195582496
x = -3.195582496

Simplifying
x = -3.195582496


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.195582496, -3.195582496}
Solution
x = {0.195582496, -3.195582496}

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