6x(5x+5)=-2

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Solution for 6x(5x+5)=-2 equation: 


Simplifying
6x(5x + 5) = -2

Reorder the terms:
6x(5 + 5x) = -2
(5 * 6x + 5x * 6x) = -2
(30x + 30x2) = -2

Solving
30x + 30x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + 30x + 30x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 30x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 15x + 15x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 15x + 15x2)' equal to zero and attempt to solve:

Simplifying
1 + 15x + 15x2 = 0

Solving
1 + 15x + 15x2 = 0

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

Divide each side by '15'.
0.06666666667 + x + x2 = 0

Move the constant term to the right:

Add '-0.06666666667' to each side of the equation.
0.06666666667 + x + -0.06666666667 + x2 = 0 + -0.06666666667

Reorder the terms:
0.06666666667 + -0.06666666667 + x + x2 = 0 + -0.06666666667

Combine like terms: 0.06666666667 + -0.06666666667 = 0.00000000000
0.00000000000 + x + x2 = 0 + -0.06666666667
x + x2 = 0 + -0.06666666667

Combine like terms: 0 + -0.06666666667 = -0.06666666667
x + x2 = -0.06666666667

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 = -0.06666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.06666666667 + 0.25

Combine like terms: -0.06666666667 + 0.25 = 0.18333333333
1.25 + x2 = 0.18333333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.18333333333

Calculate the square root of the right side: 0.428174419

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.428174419 and -0.428174419.


Subproblem 1
x + 0.5 = 0.428174419

Simplifying
x + 0.5 = 0.428174419

Reorder the terms:
0.5 + x = 0.428174419

Solving
0.5 + x = 0.428174419

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 = 0.428174419 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.428174419 + -0.5
x = 0.428174419 + -0.5

Combine like terms: 0.428174419 + -0.5 = -0.071825581
x = -0.071825581

Simplifying
x = -0.071825581


Subproblem 2
x + 0.5 = -0.428174419

Simplifying
x + 0.5 = -0.428174419

Reorder the terms:
0.5 + x = -0.428174419

Solving
0.5 + x = -0.428174419

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 = -0.428174419 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.428174419 + -0.5
x = -0.428174419 + -0.5

Combine like terms: -0.428174419 + -0.5 = -0.928174419
x = -0.928174419

Simplifying
x = -0.928174419


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.071825581, -0.928174419}
Solution
x = {-0.071825581, -0.928174419}

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