(5x+3)(3x-4)=15x*-23

Solution for (5x+3)(3x-4)=15x*-23 equation:

Simplifying
(5x + 3)(3x + -4) = 15x * -23

Reorder the terms:
(3 + 5x)(3x + -4) = 15x * -23

Reorder the terms:
(3 + 5x)(-4 + 3x) = 15x * -23

Multiply (3 + 5x) * (-4 + 3x)
(3(-4 + 3x) + 5x * (-4 + 3x)) = 15x * -23
((-4 * 3 + 3x * 3) + 5x * (-4 + 3x)) = 15x * -23
((-12 + 9x) + 5x * (-4 + 3x)) = 15x * -23
(-12 + 9x + (-4 * 5x + 3x * 5x)) = 15x * -23
(-12 + 9x + (-20x + 15x2)) = 15x * -23

Combine like terms: 9x + -20x = -11x
(-12 + -11x + 15x2) = 15x * -23

Reorder the terms for easier multiplication:
-12 + -11x + 15x2 = 15 * -23x

Multiply 15 * -23
-12 + -11x + 15x2 = -345x

Solving
-12 + -11x + 15x2 = -345x

Solving for variable 'x'.

Reorder the terms:
-12 + -11x + 345x + 15x2 = -345x + 345x

Combine like terms: -11x + 345x = 334x
-12 + 334x + 15x2 = -345x + 345x

Combine like terms: -345x + 345x = 0
-12 + 334x + 15x2 = 0

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

Divide each side by '15'.
-0.8 + 22.26666667x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 22.26666667x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 22.26666667x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 22.26666667x + x2 = 0 + 0.8
22.26666667x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
22.26666667x + x2 = 0.8

The x term is 22.26666667x.  Take half its coefficient (11.13333334).
Square it (123.9511113) and add it to both sides.

Add '123.9511113' to each side of the equation.
22.26666667x + 123.9511113 + x2 = 0.8 + 123.9511113

Reorder the terms:
123.9511113 + 22.26666667x + x2 = 0.8 + 123.9511113

Combine like terms: 0.8 + 123.9511113 = 124.7511113
123.9511113 + 22.26666667x + x2 = 124.7511113

Factor a perfect square on the left side:
(x + 11.13333334)(x + 11.13333334) = 124.7511113

Calculate the square root of the right side: 11.1692037

Break this problem into two subproblems by setting 
(x + 11.13333334) equal to 11.1692037 and -11.1692037.

Subproblem 1
x + 11.13333334 = 11.1692037

Simplifying
x + 11.13333334 = 11.1692037

Reorder the terms:
11.13333334 + x = 11.1692037

Solving
11.13333334 + x = 11.1692037

Solving for variable 'x'.

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

Add '-11.13333334' to each side of the equation.
11.13333334 + -11.13333334 + x = 11.1692037 + -11.13333334

Combine like terms: 11.13333334 + -11.13333334 = 0.00000000
0.00000000 + x = 11.1692037 + -11.13333334
x = 11.1692037 + -11.13333334

Combine like terms: 11.1692037 + -11.13333334 = 0.03587036
x = 0.03587036

Simplifying
x = 0.03587036

Subproblem 2
x + 11.13333334 = -11.1692037

Simplifying
x + 11.13333334 = -11.1692037

Reorder the terms:
11.13333334 + x = -11.1692037

Solving
11.13333334 + x = -11.1692037

Solving for variable 'x'.

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

Add '-11.13333334' to each side of the equation.
11.13333334 + -11.13333334 + x = -11.1692037 + -11.13333334

Combine like terms: 11.13333334 + -11.13333334 = 0.00000000
0.00000000 + x = -11.1692037 + -11.13333334
x = -11.1692037 + -11.13333334

Combine like terms: -11.1692037 + -11.13333334 = -22.30253704
x = -22.30253704

Simplifying
x = -22.30253704

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.03587036, -22.30253704}