10=3x(2+x)

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Solution for 10=3x(2+x) equation: 


Simplifying
10 = 3x(2 + x)
10 = (2 * 3x + x * 3x)
10 = (6x + 3x2)

Solving
10 = 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
10 + -6x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
10 + -6x + -3x2 = 0 + 3x2 + -3x2
10 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
10 + -6x + -3x2 = 0

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

Divide each side by '-3'.
-3.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 2x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 2x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 3.333333333
2x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
2x + x2 = 3.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 3.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 3.333333333 + 1

Combine like terms: 3.333333333 + 1 = 4.333333333
1 + 2x + x2 = 4.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 4.333333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(x + 1) equal to 2.081665999 and -2.081665999.


Subproblem 1
x + 1 = 2.081665999

Simplifying
x + 1 = 2.081665999

Reorder the terms:
1 + x = 2.081665999

Solving
1 + x = 2.081665999

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.081665999 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.081665999 + -1
x = 2.081665999 + -1

Combine like terms: 2.081665999 + -1 = 1.081665999
x = 1.081665999

Simplifying
x = 1.081665999


Subproblem 2
x + 1 = -2.081665999

Simplifying
x + 1 = -2.081665999

Reorder the terms:
1 + x = -2.081665999

Solving
1 + x = -2.081665999

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.081665999 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.081665999 + -1
x = -2.081665999 + -1

Combine like terms: -2.081665999 + -1 = -3.081665999
x = -3.081665999

Simplifying
x = -3.081665999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.081665999, -3.081665999}

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