6x(5x+5)=-3

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Solution for 6x(5x+5)=-3 equation: 


Simplifying
6x(5x + 5) = -3

Reorder the terms:
6x(5 + 5x) = -3
(5 * 6x + 5x * 6x) = -3
(30x + 30x2) = -3

Solving
30x + 30x2 = -3

Solving for variable 'x'.

Reorder the terms:
3 + 30x + 30x2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 30x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 10x + 10x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + 10x + 10x2)' equal to zero and attempt to solve:

Simplifying
1 + 10x + 10x2 = 0

Solving
1 + 10x + 10x2 = 0

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

Divide each side by '10'.
0.1 + x + x2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + x + -0.1 + x2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + x + x2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x + x2 = 0.0 + -0.1
x + x2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
x + x2 = -0.1

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 = -0.1 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.1 + 0.25

Combine like terms: -0.1 + 0.25 = 0.15
1.25 + x2 = 0.15

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.15

Calculate the square root of the right side: 0.387298335

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.387298335 and -0.387298335.


Subproblem 1
x + 0.5 = 0.387298335

Simplifying
x + 0.5 = 0.387298335

Reorder the terms:
0.5 + x = 0.387298335

Solving
0.5 + x = 0.387298335

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 = 0.387298335 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.387298335 + -0.5
x = 0.387298335 + -0.5

Combine like terms: 0.387298335 + -0.5 = -0.112701665
x = -0.112701665

Simplifying
x = -0.112701665


Subproblem 2
x + 0.5 = -0.387298335

Simplifying
x + 0.5 = -0.387298335

Reorder the terms:
0.5 + x = -0.387298335

Solving
0.5 + x = -0.387298335

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 = -0.387298335 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.387298335 + -0.5
x = -0.387298335 + -0.5

Combine like terms: -0.387298335 + -0.5 = -0.887298335
x = -0.887298335

Simplifying
x = -0.887298335


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.112701665, -0.887298335}
Solution
x = {-0.112701665, -0.887298335}

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