720=6x(x+20)

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Solution for 720=6x(x+20) equation:


Simplifying
720 = 6x(x + 20)

Reorder the terms:
720 = 6x(20 + x)
720 = (20 * 6x + x * 6x)
720 = (120x + 6x2)

Solving
720 = 120x + 6x2

Solving for variable 'x'.

Reorder the terms:
720 + -120x + -6x2 = 120x + -120x + 6x2 + -6x2

Combine like terms: 120x + -120x = 0
720 + -120x + -6x2 = 0 + 6x2 + -6x2
720 + -120x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
720 + -120x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(120 + -20x + -1x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(120 + -20x + -1x2)' equal to zero and attempt to solve:

Simplifying
120 + -20x + -1x2 = 0

Solving
120 + -20x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-120 + 20x + x2 = 0

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 20x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 20x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 20x + x2 = 0 + 120
20x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
20x + x2 = 120

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 120 + 100

Reorder the terms:
100 + 20x + x2 = 120 + 100

Combine like terms: 120 + 100 = 220
100 + 20x + x2 = 220

Factor a perfect square on the left side:
(x + 10)(x + 10) = 220

Calculate the square root of the right side: 14.832396974

Break this problem into two subproblems by setting 
(x + 10) equal to 14.832396974 and -14.832396974.


Subproblem 1
x + 10 = 14.832396974

Simplifying
x + 10 = 14.832396974

Reorder the terms:
10 + x = 14.832396974

Solving
10 + x = 14.832396974

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 14.832396974 + -10

Combine like terms: 10 + -10 = 0
0 + x = 14.832396974 + -10
x = 14.832396974 + -10

Combine like terms: 14.832396974 + -10 = 4.832396974
x = 4.832396974

Simplifying
x = 4.832396974


Subproblem 2
x + 10 = -14.832396974

Simplifying
x + 10 = -14.832396974

Reorder the terms:
10 + x = -14.832396974

Solving
10 + x = -14.832396974

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -14.832396974 + -10

Combine like terms: 10 + -10 = 0
0 + x = -14.832396974 + -10
x = -14.832396974 + -10

Combine like terms: -14.832396974 + -10 = -24.832396974
x = -24.832396974

Simplifying
x = -24.832396974


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.832396974, -24.832396974}
Solution
x = {4.832396974, -24.832396974}

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