12x(x+5)=8x+44

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Solution for 12x(x+5)=8x+44 equation: 


Simplifying
12x(x + 5) = 8x + 44

Reorder the terms:
12x(5 + x) = 8x + 44
(5 * 12x + x * 12x) = 8x + 44
(60x + 12x2) = 8x + 44

Reorder the terms:
60x + 12x2 = 44 + 8x

Solving
60x + 12x2 = 44 + 8x

Solving for variable 'x'.

Reorder the terms:
-44 + 60x + -8x + 12x2 = 44 + 8x + -44 + -8x

Combine like terms: 60x + -8x = 52x
-44 + 52x + 12x2 = 44 + 8x + -44 + -8x

Reorder the terms:
-44 + 52x + 12x2 = 44 + -44 + 8x + -8x

Combine like terms: 44 + -44 = 0
-44 + 52x + 12x2 = 0 + 8x + -8x
-44 + 52x + 12x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-44 + 52x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + 13x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-11 + 13x + 3x2)' equal to zero and attempt to solve:

Simplifying
-11 + 13x + 3x2 = 0

Solving
-11 + 13x + 3x2 = 0

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

Divide each side by '3'.
-3.666666667 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + 4.333333333x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + 4.333333333x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + 4.333333333x + x2 = 0 + 3.666666667
4.333333333x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
4.333333333x + x2 = 3.666666667

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 3.666666667 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 3.666666667 + 4.694444446

Combine like terms: 3.666666667 + 4.694444446 = 8.361111113
4.694444446 + 4.333333333x + x2 = 8.361111113

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 8.361111113

Calculate the square root of the right side: 2.891558596

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 2.891558596 and -2.891558596.


Subproblem 1
x + 2.166666667 = 2.891558596

Simplifying
x + 2.166666667 = 2.891558596

Reorder the terms:
2.166666667 + x = 2.891558596

Solving
2.166666667 + x = 2.891558596

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 2.891558596 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 2.891558596 + -2.166666667
x = 2.891558596 + -2.166666667

Combine like terms: 2.891558596 + -2.166666667 = 0.724891929
x = 0.724891929

Simplifying
x = 0.724891929


Subproblem 2
x + 2.166666667 = -2.891558596

Simplifying
x + 2.166666667 = -2.891558596

Reorder the terms:
2.166666667 + x = -2.891558596

Solving
2.166666667 + x = -2.891558596

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -2.891558596 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -2.891558596 + -2.166666667
x = -2.891558596 + -2.166666667

Combine like terms: -2.891558596 + -2.166666667 = -5.058225263
x = -5.058225263

Simplifying
x = -5.058225263


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.724891929, -5.058225263}
Solution
x = {0.724891929, -5.058225263}

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