7x(5x)+3x=2x+15

Solution for 7x(5x)+3x=2x+15 equation:

Simplifying
7x(5x) + 3x = 2x + 15

Remove parenthesis around (5x)
7x * 5x + 3x = 2x + 15

Reorder the terms for easier multiplication:
7 * 5x * x + 3x = 2x + 15

Multiply 7 * 5
35x * x + 3x = 2x + 15

Multiply x * x
35x2 + 3x = 2x + 15

Reorder the terms:
3x + 35x2 = 2x + 15

Reorder the terms:
3x + 35x2 = 15 + 2x

Solving
3x + 35x2 = 15 + 2x

Solving for variable 'x'.

Reorder the terms:
-15 + 3x + -2x + 35x2 = 15 + 2x + -15 + -2x

Combine like terms: 3x + -2x = 1x
-15 + 1x + 35x2 = 15 + 2x + -15 + -2x

Reorder the terms:
-15 + 1x + 35x2 = 15 + -15 + 2x + -2x

Combine like terms: 15 + -15 = 0
-15 + 1x + 35x2 = 0 + 2x + -2x
-15 + 1x + 35x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-15 + 1x + 35x2 = 0

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

Divide each side by '35'.
-0.4285714286 + 0.02857142857x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.02857142857x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + 0.02857142857x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + 0.02857142857x + x2 = 0 + 0.4285714286
0.02857142857x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
0.02857142857x + x2 = 0.4285714286

The x term is 0.02857142857x.  Take half its coefficient (0.01428571429).
Square it (0.0002040816328) and add it to both sides.

Add '0.0002040816328' to each side of the equation.
0.02857142857x + 0.0002040816328 + x2 = 0.4285714286 + 0.0002040816328

Reorder the terms:
0.0002040816328 + 0.02857142857x + x2 = 0.4285714286 + 0.0002040816328

Combine like terms: 0.4285714286 + 0.0002040816328 = 0.4287755102328
0.0002040816328 + 0.02857142857x + x2 = 0.4287755102328

Factor a perfect square on the left side:
(x + 0.01428571429)(x + 0.01428571429) = 0.4287755102328

Calculate the square root of the right side: 0.654809522

Break this problem into two subproblems by setting 
(x + 0.01428571429) equal to 0.654809522 and -0.654809522.

Subproblem 1
x + 0.01428571429 = 0.654809522

Simplifying
x + 0.01428571429 = 0.654809522

Reorder the terms:
0.01428571429 + x = 0.654809522

Solving
0.01428571429 + x = 0.654809522

Solving for variable 'x'.

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

Add '-0.01428571429' to each side of the equation.
0.01428571429 + -0.01428571429 + x = 0.654809522 + -0.01428571429

Combine like terms: 0.01428571429 + -0.01428571429 = 0.00000000000
0.00000000000 + x = 0.654809522 + -0.01428571429
x = 0.654809522 + -0.01428571429

Combine like terms: 0.654809522 + -0.01428571429 = 0.64052380771
x = 0.64052380771

Simplifying
x = 0.64052380771

Subproblem 2
x + 0.01428571429 = -0.654809522

Simplifying
x + 0.01428571429 = -0.654809522

Reorder the terms:
0.01428571429 + x = -0.654809522

Solving
0.01428571429 + x = -0.654809522

Solving for variable 'x'.

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

Add '-0.01428571429' to each side of the equation.
0.01428571429 + -0.01428571429 + x = -0.654809522 + -0.01428571429

Combine like terms: 0.01428571429 + -0.01428571429 = 0.00000000000
0.00000000000 + x = -0.654809522 + -0.01428571429
x = -0.654809522 + -0.01428571429

Combine like terms: -0.654809522 + -0.01428571429 = -0.66909523629
x = -0.66909523629

Simplifying
x = -0.66909523629

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.64052380771, -0.66909523629}