6x^2+60x+10=0

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Solution for 6x^2+60x+10=0 equation: 


Simplifying
6x2 + 60x + 10 = 0

Reorder the terms:
10 + 60x + 6x2 = 0

Solving
10 + 60x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 30x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 30x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + 30x + 3x2 = 0

Solving
5 + 30x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 10x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 10x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 10x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 10x + x2 = 0 + -1.666666667
10x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
10x + x2 = -1.666666667

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -1.666666667 + 25

Reorder the terms:
25 + 10x + x2 = -1.666666667 + 25

Combine like terms: -1.666666667 + 25 = 23.333333333
25 + 10x + x2 = 23.333333333

Factor a perfect square on the left side:
(x + 5)(x + 5) = 23.333333333

Calculate the square root of the right side: 4.830458915

Break this problem into two subproblems by setting 
(x + 5) equal to 4.830458915 and -4.830458915.


Subproblem 1
x + 5 = 4.830458915

Simplifying
x + 5 = 4.830458915

Reorder the terms:
5 + x = 4.830458915

Solving
5 + x = 4.830458915

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 4.830458915 + -5

Combine like terms: 5 + -5 = 0
0 + x = 4.830458915 + -5
x = 4.830458915 + -5

Combine like terms: 4.830458915 + -5 = -0.169541085
x = -0.169541085

Simplifying
x = -0.169541085


Subproblem 2
x + 5 = -4.830458915

Simplifying
x + 5 = -4.830458915

Reorder the terms:
5 + x = -4.830458915

Solving
5 + x = -4.830458915

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -4.830458915 + -5

Combine like terms: 5 + -5 = 0
0 + x = -4.830458915 + -5
x = -4.830458915 + -5

Combine like terms: -4.830458915 + -5 = -9.830458915
x = -9.830458915

Simplifying
x = -9.830458915


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.169541085, -9.830458915}
Solution
x = {-0.169541085, -9.830458915}

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