(x+7)(15x)=512

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Solution for (x+7)(15x)=512 equation: 


Simplifying
(x + 7)(15x) = 512

Reorder the terms:
(7 + x)(15x) = 512

Remove parenthesis around (15x)
(7 + x) * 15x = 512

Reorder the terms for easier multiplication:
15x(7 + x) = 512
(7 * 15x + x * 15x) = 512
(105x + 15x2) = 512

Solving
105x + 15x2 = 512

Solving for variable 'x'.

Reorder the terms:
-512 + 105x + 15x2 = 512 + -512

Combine like terms: 512 + -512 = 0
-512 + 105x + 15x2 = 0

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

Divide each side by '15'.
-34.13333333 + 7x + x2 = 0

Move the constant term to the right:

Add '34.13333333' to each side of the equation.
-34.13333333 + 7x + 34.13333333 + x2 = 0 + 34.13333333

Reorder the terms:
-34.13333333 + 34.13333333 + 7x + x2 = 0 + 34.13333333

Combine like terms: -34.13333333 + 34.13333333 = 0.00000000
0.00000000 + 7x + x2 = 0 + 34.13333333
7x + x2 = 0 + 34.13333333

Combine like terms: 0 + 34.13333333 = 34.13333333
7x + x2 = 34.13333333

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 34.13333333 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 34.13333333 + 12.25

Combine like terms: 34.13333333 + 12.25 = 46.38333333
12.25 + 7x + x2 = 46.38333333

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 46.38333333

Calculate the square root of the right side: 6.810531061

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.810531061 and -6.810531061.


Subproblem 1
x + 3.5 = 6.810531061

Simplifying
x + 3.5 = 6.810531061

Reorder the terms:
3.5 + x = 6.810531061

Solving
3.5 + x = 6.810531061

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 6.810531061 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 6.810531061 + -3.5
x = 6.810531061 + -3.5

Combine like terms: 6.810531061 + -3.5 = 3.310531061
x = 3.310531061

Simplifying
x = 3.310531061


Subproblem 2
x + 3.5 = -6.810531061

Simplifying
x + 3.5 = -6.810531061

Reorder the terms:
3.5 + x = -6.810531061

Solving
3.5 + x = -6.810531061

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -6.810531061 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -6.810531061 + -3.5
x = -6.810531061 + -3.5

Combine like terms: -6.810531061 + -3.5 = -10.310531061
x = -10.310531061

Simplifying
x = -10.310531061


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.310531061, -10.310531061}

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