4x(3x+3)=10

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Solution for 4x(3x+3)=10 equation: 


Simplifying
4x(3x + 3) = 10

Reorder the terms:
4x(3 + 3x) = 10
(3 * 4x + 3x * 4x) = 10
(12x + 12x2) = 10

Solving
12x + 12x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 12x + 12x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 12x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 6x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 6x + 6x2)' equal to zero and attempt to solve:

Simplifying
-5 + 6x + 6x2 = 0

Solving
-5 + 6x + 6x2 = 0

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

Divide each side by '6'.
-0.8333333333 + x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + x + x2 = 0 + 0.8333333333
x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
x + x2 = 0.8333333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.8333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.8333333333 + 0.25

Combine like terms: 0.8333333333 + 0.25 = 1.0833333333
1.25 + x2 = 1.0833333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.0833333333

Calculate the square root of the right side: 1.040833

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.040833 and -1.040833.


Subproblem 1
x + 0.5 = 1.040833

Simplifying
x + 0.5 = 1.040833

Reorder the terms:
0.5 + x = 1.040833

Solving
0.5 + x = 1.040833

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.040833 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.040833 + -0.5
x = 1.040833 + -0.5

Combine like terms: 1.040833 + -0.5 = 0.540833
x = 0.540833

Simplifying
x = 0.540833


Subproblem 2
x + 0.5 = -1.040833

Simplifying
x + 0.5 = -1.040833

Reorder the terms:
0.5 + x = -1.040833

Solving
0.5 + x = -1.040833

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.040833 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.040833 + -0.5
x = -1.040833 + -0.5

Combine like terms: -1.040833 + -0.5 = -1.540833
x = -1.540833

Simplifying
x = -1.540833


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.540833, -1.540833}
Solution
x = {0.540833, -1.540833}

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