(2x+15)*(x+10)=(3x+15)*(x+5)

Solution for (2x+15)*(x+10)=(3x+15)*(x+5) equation:

Simplifying
(2x + 15)(x + 10) = (3x + 15)(x + 5)

Reorder the terms:
(15 + 2x)(x + 10) = (3x + 15)(x + 5)

Reorder the terms:
(15 + 2x)(10 + x) = (3x + 15)(x + 5)

Multiply (15 + 2x) * (10 + x)
(15(10 + x) + 2x * (10 + x)) = (3x + 15)(x + 5)
((10 * 15 + x * 15) + 2x * (10 + x)) = (3x + 15)(x + 5)
((150 + 15x) + 2x * (10 + x)) = (3x + 15)(x + 5)
(150 + 15x + (10 * 2x + x * 2x)) = (3x + 15)(x + 5)
(150 + 15x + (20x + 2x2)) = (3x + 15)(x + 5)

Combine like terms: 15x + 20x = 35x
(150 + 35x + 2x2) = (3x + 15)(x + 5)

Reorder the terms:
150 + 35x + 2x2 = (15 + 3x)(x + 5)

Reorder the terms:
150 + 35x + 2x2 = (15 + 3x)(5 + x)

Multiply (15 + 3x) * (5 + x)
150 + 35x + 2x2 = (15(5 + x) + 3x * (5 + x))
150 + 35x + 2x2 = ((5 * 15 + x * 15) + 3x * (5 + x))
150 + 35x + 2x2 = ((75 + 15x) + 3x * (5 + x))
150 + 35x + 2x2 = (75 + 15x + (5 * 3x + x * 3x))
150 + 35x + 2x2 = (75 + 15x + (15x + 3x2))

Combine like terms: 15x + 15x = 30x
150 + 35x + 2x2 = (75 + 30x + 3x2)

Solving
150 + 35x + 2x2 = 75 + 30x + 3x2

Solving for variable 'x'.

Reorder the terms:
150 + -75 + 35x + -30x + 2x2 + -3x2 = 75 + 30x + 3x2 + -75 + -30x + -3x2

Combine like terms: 150 + -75 = 75
75 + 35x + -30x + 2x2 + -3x2 = 75 + 30x + 3x2 + -75 + -30x + -3x2

Combine like terms: 35x + -30x = 5x
75 + 5x + 2x2 + -3x2 = 75 + 30x + 3x2 + -75 + -30x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
75 + 5x + -1x2 = 75 + 30x + 3x2 + -75 + -30x + -3x2

Reorder the terms:
75 + 5x + -1x2 = 75 + -75 + 30x + -30x + 3x2 + -3x2

Combine like terms: 75 + -75 = 0
75 + 5x + -1x2 = 0 + 30x + -30x + 3x2 + -3x2
75 + 5x + -1x2 = 30x + -30x + 3x2 + -3x2

Combine like terms: 30x + -30x = 0
75 + 5x + -1x2 = 0 + 3x2 + -3x2
75 + 5x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
75 + 5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-75 + -5x + x2 = 0

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -5x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + -5x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -5x + x2 = 0 + 75
-5x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
-5x + x2 = 75

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 75 + 6.25

Combine like terms: 75 + 6.25 = 81.25
6.25 + -5x + x2 = 81.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(x + -2.5) equal to 9.013878189 and -9.013878189.

Subproblem 1
x + -2.5 = 9.013878189

Simplifying
x + -2.5 = 9.013878189

Reorder the terms:
-2.5 + x = 9.013878189

Solving
-2.5 + x = 9.013878189

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 9.013878189 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 9.013878189 + 2.5
x = 9.013878189 + 2.5

Combine like terms: 9.013878189 + 2.5 = 11.513878189
x = 11.513878189

Simplifying
x = 11.513878189

Subproblem 2
x + -2.5 = -9.013878189

Simplifying
x + -2.5 = -9.013878189

Reorder the terms:
-2.5 + x = -9.013878189

Solving
-2.5 + x = -9.013878189

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -9.013878189 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -9.013878189 + 2.5
x = -9.013878189 + 2.5

Combine like terms: -9.013878189 + 2.5 = -6.513878189
x = -6.513878189

Simplifying
x = -6.513878189

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.513878189, -6.513878189}