315=(x+2)(3x)

Solution for 315=(x+2)(3x) equation:

Simplifying
315 = (x + 2)(3x)

Reorder the terms:
315 = (2 + x)(3x)

Remove parenthesis around (3x)
315 = (2 + x) * 3x

Reorder the terms for easier multiplication:
315 = 3x(2 + x)
315 = (2 * 3x + x * 3x)
315 = (6x + 3x2)

Solving
315 = 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
315 + -6x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
315 + -6x + -3x2 = 0 + 3x2 + -3x2
315 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
315 + -6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(105 + -2x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(105 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
105 + -2x + -1x2 = 0

Solving
105 + -2x + -1x2 = 0

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

Divide each side by '-1'.
-105 + 2x + x2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 2x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 2x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 2x + x2 = 0 + 105
2x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
2x + x2 = 105

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 = 105 + 1

Reorder the terms:
1 + 2x + x2 = 105 + 1

Combine like terms: 105 + 1 = 106
1 + 2x + x2 = 106

Factor a perfect square on the left side:
(x + 1)(x + 1) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + 1) equal to 10.295630141 and -10.295630141.

Subproblem 1
x + 1 = 10.295630141

Simplifying
x + 1 = 10.295630141

Reorder the terms:
1 + x = 10.295630141

Solving
1 + x = 10.295630141

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 = 10.295630141 + -1

Combine like terms: 1 + -1 = 0
0 + x = 10.295630141 + -1
x = 10.295630141 + -1

Combine like terms: 10.295630141 + -1 = 9.295630141
x = 9.295630141

Simplifying
x = 9.295630141

Subproblem 2
x + 1 = -10.295630141

Simplifying
x + 1 = -10.295630141

Reorder the terms:
1 + x = -10.295630141

Solving
1 + x = -10.295630141

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 = -10.295630141 + -1

Combine like terms: 1 + -1 = 0
0 + x = -10.295630141 + -1
x = -10.295630141 + -1

Combine like terms: -10.295630141 + -1 = -11.295630141
x = -11.295630141

Simplifying
x = -11.295630141

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.295630141, -11.295630141}
Solution
x = {9.295630141, -11.295630141}