x(x+6)=5(20)

Solution for x(x+6)=5(20) equation:

Simplifying
x(x + 6) = 5(20)

Reorder the terms:
x(6 + x) = 5(20)
(6 * x + x * x) = 5(20)
(6x + x2) = 5(20)

Multiply 5 * 20
6x + x2 = 100

Solving
6x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 6x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 6x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 6x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 6x + x2 = 0 + 100
6x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
6x + x2 = 100

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 = 100 + 9

Reorder the terms:
9 + 6x + x2 = 100 + 9

Combine like terms: 100 + 9 = 109
9 + 6x + x2 = 109

Factor a perfect square on the left side:
(x + 3)(x + 3) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(x + 3) equal to 10.440306509 and -10.440306509.

Subproblem 1
x + 3 = 10.440306509

Simplifying
x + 3 = 10.440306509

Reorder the terms:
3 + x = 10.440306509

Solving
3 + x = 10.440306509

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 = 10.440306509 + -3

Combine like terms: 3 + -3 = 0
0 + x = 10.440306509 + -3
x = 10.440306509 + -3

Combine like terms: 10.440306509 + -3 = 7.440306509
x = 7.440306509

Simplifying
x = 7.440306509

Subproblem 2
x + 3 = -10.440306509

Simplifying
x + 3 = -10.440306509

Reorder the terms:
3 + x = -10.440306509

Solving
3 + x = -10.440306509

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 = -10.440306509 + -3

Combine like terms: 3 + -3 = 0
0 + x = -10.440306509 + -3
x = -10.440306509 + -3

Combine like terms: -10.440306509 + -3 = -13.440306509
x = -13.440306509

Simplifying
x = -13.440306509

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.440306509, -13.440306509}