3(8+2x)(5+2x)=(14.5+2x)(15+2x)

Solution for 3(8+2x)(5+2x)=(14.5+2x)(15+2x) equation:

Simplifying
3(8 + 2x)(5 + 2x) = (14.5 + 2x)(15 + 2x)

Multiply (8 + 2x) * (5 + 2x)
3(8(5 + 2x) + 2x * (5 + 2x)) = (14.5 + 2x)(15 + 2x)
3((5 * 8 + 2x * 8) + 2x * (5 + 2x)) = (14.5 + 2x)(15 + 2x)
3((40 + 16x) + 2x * (5 + 2x)) = (14.5 + 2x)(15 + 2x)
3(40 + 16x + (5 * 2x + 2x * 2x)) = (14.5 + 2x)(15 + 2x)
3(40 + 16x + (10x + 4x2)) = (14.5 + 2x)(15 + 2x)

Combine like terms: 16x + 10x = 26x
3(40 + 26x + 4x2) = (14.5 + 2x)(15 + 2x)
(40 * 3 + 26x * 3 + 4x2 * 3) = (14.5 + 2x)(15 + 2x)
(120 + 78x + 12x2) = (14.5 + 2x)(15 + 2x)

Multiply (14.5 + 2x) * (15 + 2x)
120 + 78x + 12x2 = (14.5(15 + 2x) + 2x * (15 + 2x))
120 + 78x + 12x2 = ((15 * 14.5 + 2x * 14.5) + 2x * (15 + 2x))
120 + 78x + 12x2 = ((217.5 + 29x) + 2x * (15 + 2x))
120 + 78x + 12x2 = (217.5 + 29x + (15 * 2x + 2x * 2x))
120 + 78x + 12x2 = (217.5 + 29x + (30x + 4x2))

Combine like terms: 29x + 30x = 59x
120 + 78x + 12x2 = (217.5 + 59x + 4x2)

Solving
120 + 78x + 12x2 = 217.5 + 59x + 4x2

Solving for variable 'x'.

Reorder the terms:
120 + -217.5 + 78x + -59x + 12x2 + -4x2 = 217.5 + 59x + 4x2 + -217.5 + -59x + -4x2

Combine like terms: 120 + -217.5 = -97.5
-97.5 + 78x + -59x + 12x2 + -4x2 = 217.5 + 59x + 4x2 + -217.5 + -59x + -4x2

Combine like terms: 78x + -59x = 19x
-97.5 + 19x + 12x2 + -4x2 = 217.5 + 59x + 4x2 + -217.5 + -59x + -4x2

Combine like terms: 12x2 + -4x2 = 8x2
-97.5 + 19x + 8x2 = 217.5 + 59x + 4x2 + -217.5 + -59x + -4x2

Reorder the terms:
-97.5 + 19x + 8x2 = 217.5 + -217.5 + 59x + -59x + 4x2 + -4x2

Combine like terms: 217.5 + -217.5 = 0.0
-97.5 + 19x + 8x2 = 0.0 + 59x + -59x + 4x2 + -4x2
-97.5 + 19x + 8x2 = 59x + -59x + 4x2 + -4x2

Combine like terms: 59x + -59x = 0
-97.5 + 19x + 8x2 = 0 + 4x2 + -4x2
-97.5 + 19x + 8x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-97.5 + 19x + 8x2 = 0

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

Divide each side by '8'.
-12.1875 + 2.375x + x2 = 0

Move the constant term to the right:

Add '12.1875' to each side of the equation.
-12.1875 + 2.375x + 12.1875 + x2 = 0 + 12.1875

Reorder the terms:
-12.1875 + 12.1875 + 2.375x + x2 = 0 + 12.1875

Combine like terms: -12.1875 + 12.1875 = 0.0000
0.0000 + 2.375x + x2 = 0 + 12.1875
2.375x + x2 = 0 + 12.1875

Combine like terms: 0 + 12.1875 = 12.1875
2.375x + x2 = 12.1875

The x term is 2.375x.  Take half its coefficient (1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
2.375x + 1.41015625 + x2 = 12.1875 + 1.41015625

Reorder the terms:
1.41015625 + 2.375x + x2 = 12.1875 + 1.41015625

Combine like terms: 12.1875 + 1.41015625 = 13.59765625
1.41015625 + 2.375x + x2 = 13.59765625

Factor a perfect square on the left side:
(x + 1.1875)(x + 1.1875) = 13.59765625

Calculate the square root of the right side: 3.6875

Break this problem into two subproblems by setting 
(x + 1.1875) equal to 3.6875 and -3.6875.

Subproblem 1
x + 1.1875 = 3.6875

Simplifying
x + 1.1875 = 3.6875

Reorder the terms:
1.1875 + x = 3.6875

Solving
1.1875 + x = 3.6875

Solving for variable 'x'.

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

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + x = 3.6875 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + x = 3.6875 + -1.1875
x = 3.6875 + -1.1875

Combine like terms: 3.6875 + -1.1875 = 2.5
x = 2.5

Simplifying
x = 2.5

Subproblem 2
x + 1.1875 = -3.6875

Simplifying
x + 1.1875 = -3.6875

Reorder the terms:
1.1875 + x = -3.6875

Solving
1.1875 + x = -3.6875

Solving for variable 'x'.

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

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + x = -3.6875 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + x = -3.6875 + -1.1875
x = -3.6875 + -1.1875

Combine like terms: -3.6875 + -1.1875 = -4.875
x = -4.875

Simplifying
x = -4.875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5, -4.875}