(3x+5)*(3x+5x)=169+30x

Solution for (3x+5)*(3x+5x)=169+30x equation:

Simplifying
(3x + 5)(3x + 5x) = 169 + 30x

Reorder the terms:
(5 + 3x)(3x + 5x) = 169 + 30x

Combine like terms: 3x + 5x = 8x
(5 + 3x)(8x) = 169 + 30x

Remove parenthesis around (8x)
(5 + 3x) * 8x = 169 + 30x

Reorder the terms for easier multiplication:
8x(5 + 3x) = 169 + 30x
(5 * 8x + 3x * 8x) = 169 + 30x
(40x + 24x2) = 169 + 30x

Solving
40x + 24x2 = 169 + 30x

Solving for variable 'x'.

Reorder the terms:
-169 + 40x + -30x + 24x2 = 169 + 30x + -169 + -30x

Combine like terms: 40x + -30x = 10x
-169 + 10x + 24x2 = 169 + 30x + -169 + -30x

Reorder the terms:
-169 + 10x + 24x2 = 169 + -169 + 30x + -30x

Combine like terms: 169 + -169 = 0
-169 + 10x + 24x2 = 0 + 30x + -30x
-169 + 10x + 24x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
-169 + 10x + 24x2 = 0

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

Divide each side by '24'.
-7.041666667 + 0.4166666667x + x2 = 0

Move the constant term to the right:

Add '7.041666667' to each side of the equation.
-7.041666667 + 0.4166666667x + 7.041666667 + x2 = 0 + 7.041666667

Reorder the terms:
-7.041666667 + 7.041666667 + 0.4166666667x + x2 = 0 + 7.041666667

Combine like terms: -7.041666667 + 7.041666667 = 0.000000000
0.000000000 + 0.4166666667x + x2 = 0 + 7.041666667
0.4166666667x + x2 = 0 + 7.041666667

Combine like terms: 0 + 7.041666667 = 7.041666667
0.4166666667x + x2 = 7.041666667

The x term is 0.4166666667x.  Take half its coefficient (0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
0.4166666667x + 0.04340277781 + x2 = 7.041666667 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667x + x2 = 7.041666667 + 0.04340277781

Combine like terms: 7.041666667 + 0.04340277781 = 7.08506944481
0.04340277781 + 0.4166666667x + x2 = 7.08506944481

Factor a perfect square on the left side:
(x + 0.2083333334)(x + 0.2083333334) = 7.08506944481

Calculate the square root of the right side: 2.661779376

Break this problem into two subproblems by setting 
(x + 0.2083333334) equal to 2.661779376 and -2.661779376.

Subproblem 1
x + 0.2083333334 = 2.661779376

Simplifying
x + 0.2083333334 = 2.661779376

Reorder the terms:
0.2083333334 + x = 2.661779376

Solving
0.2083333334 + x = 2.661779376

Solving for variable 'x'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + x = 2.661779376 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + x = 2.661779376 + -0.2083333334
x = 2.661779376 + -0.2083333334

Combine like terms: 2.661779376 + -0.2083333334 = 2.4534460426
x = 2.4534460426

Simplifying
x = 2.4534460426

Subproblem 2
x + 0.2083333334 = -2.661779376

Simplifying
x + 0.2083333334 = -2.661779376

Reorder the terms:
0.2083333334 + x = -2.661779376

Solving
0.2083333334 + x = -2.661779376

Solving for variable 'x'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + x = -2.661779376 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + x = -2.661779376 + -0.2083333334
x = -2.661779376 + -0.2083333334

Combine like terms: -2.661779376 + -0.2083333334 = -2.8701127094
x = -2.8701127094

Simplifying
x = -2.8701127094

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.4534460426, -2.8701127094}