0.25x(x+6)+6=10

Solution for 0.25x(x+6)+6=10 equation:

Simplifying
0.25x(x + 6) + 6 = 10

Reorder the terms:
0.25x(6 + x) + 6 = 10
(6 * 0.25x + x * 0.25x) + 6 = 10
(1.5x + 0.25x2) + 6 = 10

Reorder the terms:
6 + 1.5x + 0.25x2 = 10

Solving
6 + 1.5x + 0.25x2 = 10

Solving for variable 'x'.

Reorder the terms:
6 + -10 + 1.5x + 0.25x2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + 1.5x + 0.25x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + 1.5x + 0.25x2 = 0

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

Divide each side by '0.25'.
-16 + 6x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 6x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 6x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 6x + x2 = 0 + 16
6x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
6x + x2 = 16

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 16 + 9

Reorder the terms:
9 + 6x + x2 = 16 + 9

Combine like terms: 16 + 9 = 25
9 + 6x + x2 = 25

Factor a perfect square on the left side:
(x + 3)(x + 3) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 3) equal to 5 and -5.

Subproblem 1
x + 3 = 5

Simplifying
x + 3 = 5

Reorder the terms:
3 + x = 5

Solving
3 + x = 5

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 5 + -3

Combine like terms: 3 + -3 = 0
0 + x = 5 + -3
x = 5 + -3

Combine like terms: 5 + -3 = 2
x = 2

Simplifying
x = 2

Subproblem 2
x + 3 = -5

Simplifying
x + 3 = -5

Reorder the terms:
3 + x = -5

Solving
3 + x = -5

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -5 + -3

Combine like terms: 3 + -3 = 0
0 + x = -5 + -3
x = -5 + -3

Combine like terms: -5 + -3 = -8
x = -8

Simplifying
x = -8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -8}