(x+15)(1.25x+15)=3(1.25x(x))

Solution for (x+15)(1.25x+15)=3(1.25x(x)) equation:

Simplifying
(x + 15)(1.25x + 15) = 3(1.25x(x))

Reorder the terms:
(15 + x)(1.25x + 15) = 3(1.25x(x))

Reorder the terms:
(15 + x)(15 + 1.25x) = 3(1.25x(x))

Multiply (15 + x) * (15 + 1.25x)
(15(15 + 1.25x) + x(15 + 1.25x)) = 3(1.25x(x))
((15 * 15 + 1.25x * 15) + x(15 + 1.25x)) = 3(1.25x(x))
((225 + 18.75x) + x(15 + 1.25x)) = 3(1.25x(x))
(225 + 18.75x + (15 * x + 1.25x * x)) = 3(1.25x(x))
(225 + 18.75x + (15x + 1.25x2)) = 3(1.25x(x))

Combine like terms: 18.75x + 15x = 33.75x
(225 + 33.75x + 1.25x2) = 3(1.25x(x))

Multiply x * x
225 + 33.75x + 1.25x2 = 3(1.25x2)

Remove parenthesis around (1.25x2)
225 + 33.75x + 1.25x2 = 3 * 1.25x2

Multiply 3 * 1.25
225 + 33.75x + 1.25x2 = 3.75x2

Solving
225 + 33.75x + 1.25x2 = 3.75x2

Solving for variable 'x'.

Combine like terms: 1.25x2 + -3.75x2 = -2.5x2
225 + 33.75x + -2.5x2 = 3.75x2 + -3.75x2

Combine like terms: 3.75x2 + -3.75x2 = 0.00
225 + 33.75x + -2.5x2 = 0.00

Begin completing the square.  Divide all terms by
-2.5 the coefficient of the squared term: 

Divide each side by '-2.5'.
-90 + -13.5x + x2 = 0.0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -13.5x + 90 + x2 = 0.0 + 90

Reorder the terms:
-90 + 90 + -13.5x + x2 = 0.0 + 90

Combine like terms: -90 + 90 = 0
0 + -13.5x + x2 = 0.0 + 90
-13.5x + x2 = 0.0 + 90

Combine like terms: 0.0 + 90 = 90
-13.5x + x2 = 90

The x term is -13.5x.  Take half its coefficient (-6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
-13.5x + 45.5625 + x2 = 90 + 45.5625

Reorder the terms:
45.5625 + -13.5x + x2 = 90 + 45.5625

Combine like terms: 90 + 45.5625 = 135.5625
45.5625 + -13.5x + x2 = 135.5625

Factor a perfect square on the left side:
(x + -6.75)(x + -6.75) = 135.5625

Calculate the square root of the right side: 11.643131022

Break this problem into two subproblems by setting 
(x + -6.75) equal to 11.643131022 and -11.643131022.

Subproblem 1
x + -6.75 = 11.643131022

Simplifying
x + -6.75 = 11.643131022

Reorder the terms:
-6.75 + x = 11.643131022

Solving
-6.75 + x = 11.643131022

Solving for variable 'x'.

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

Add '6.75' to each side of the equation.
-6.75 + 6.75 + x = 11.643131022 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + x = 11.643131022 + 6.75
x = 11.643131022 + 6.75

Combine like terms: 11.643131022 + 6.75 = 18.393131022
x = 18.393131022

Simplifying
x = 18.393131022

Subproblem 2
x + -6.75 = -11.643131022

Simplifying
x + -6.75 = -11.643131022

Reorder the terms:
-6.75 + x = -11.643131022

Solving
-6.75 + x = -11.643131022

Solving for variable 'x'.

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

Add '6.75' to each side of the equation.
-6.75 + 6.75 + x = -11.643131022 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + x = -11.643131022 + 6.75
x = -11.643131022 + 6.75

Combine like terms: -11.643131022 + 6.75 = -4.893131022
x = -4.893131022

Simplifying
x = -4.893131022

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.393131022, -4.893131022}