2(x+5)+3(2x-3)=6(2x-3)*(x+5)

Solution for 2(x+5)+3(2x-3)=6(2x-3)*(x+5) equation:

Simplifying
2(x + 5) + 3(2x + -3) = 6(2x + -3)(x + 5)

Reorder the terms:
2(5 + x) + 3(2x + -3) = 6(2x + -3)(x + 5)
(5 * 2 + x * 2) + 3(2x + -3) = 6(2x + -3)(x + 5)
(10 + 2x) + 3(2x + -3) = 6(2x + -3)(x + 5)

Reorder the terms:
10 + 2x + 3(-3 + 2x) = 6(2x + -3)(x + 5)
10 + 2x + (-3 * 3 + 2x * 3) = 6(2x + -3)(x + 5)
10 + 2x + (-9 + 6x) = 6(2x + -3)(x + 5)

Reorder the terms:
10 + -9 + 2x + 6x = 6(2x + -3)(x + 5)

Combine like terms: 10 + -9 = 1
1 + 2x + 6x = 6(2x + -3)(x + 5)

Combine like terms: 2x + 6x = 8x
1 + 8x = 6(2x + -3)(x + 5)

Reorder the terms:
1 + 8x = 6(-3 + 2x)(x + 5)

Reorder the terms:
1 + 8x = 6(-3 + 2x)(5 + x)

Multiply (-3 + 2x) * (5 + x)
1 + 8x = 6(-3(5 + x) + 2x * (5 + x))
1 + 8x = 6((5 * -3 + x * -3) + 2x * (5 + x))
1 + 8x = 6((-15 + -3x) + 2x * (5 + x))
1 + 8x = 6(-15 + -3x + (5 * 2x + x * 2x))
1 + 8x = 6(-15 + -3x + (10x + 2x2))

Combine like terms: -3x + 10x = 7x
1 + 8x = 6(-15 + 7x + 2x2)
1 + 8x = (-15 * 6 + 7x * 6 + 2x2 * 6)
1 + 8x = (-90 + 42x + 12x2)

Solving
1 + 8x = -90 + 42x + 12x2

Solving for variable 'x'.

Reorder the terms:
1 + 90 + 8x + -42x + -12x2 = -90 + 42x + 12x2 + 90 + -42x + -12x2

Combine like terms: 1 + 90 = 91
91 + 8x + -42x + -12x2 = -90 + 42x + 12x2 + 90 + -42x + -12x2

Combine like terms: 8x + -42x = -34x
91 + -34x + -12x2 = -90 + 42x + 12x2 + 90 + -42x + -12x2

Reorder the terms:
91 + -34x + -12x2 = -90 + 90 + 42x + -42x + 12x2 + -12x2

Combine like terms: -90 + 90 = 0
91 + -34x + -12x2 = 0 + 42x + -42x + 12x2 + -12x2
91 + -34x + -12x2 = 42x + -42x + 12x2 + -12x2

Combine like terms: 42x + -42x = 0
91 + -34x + -12x2 = 0 + 12x2 + -12x2
91 + -34x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
91 + -34x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-7.583333333 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '7.583333333' to each side of the equation.
-7.583333333 + 2.833333333x + 7.583333333 + x2 = 0 + 7.583333333

Reorder the terms:
-7.583333333 + 7.583333333 + 2.833333333x + x2 = 0 + 7.583333333

Combine like terms: -7.583333333 + 7.583333333 = 0.000000000
0.000000000 + 2.833333333x + x2 = 0 + 7.583333333
2.833333333x + x2 = 0 + 7.583333333

Combine like terms: 0 + 7.583333333 = 7.583333333
2.833333333x + x2 = 7.583333333

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = 7.583333333 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = 7.583333333 + 2.006944445

Combine like terms: 7.583333333 + 2.006944445 = 9.590277778
2.006944445 + 2.833333333x + x2 = 9.590277778

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = 9.590277778

Calculate the square root of the right side: 3.096817363

Break this problem into two subproblems by setting 
(x + 1.416666667) equal to 3.096817363 and -3.096817363.

Subproblem 1
x + 1.416666667 = 3.096817363

Simplifying
x + 1.416666667 = 3.096817363

Reorder the terms:
1.416666667 + x = 3.096817363

Solving
1.416666667 + x = 3.096817363

Solving for variable 'x'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + x = 3.096817363 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + x = 3.096817363 + -1.416666667
x = 3.096817363 + -1.416666667

Combine like terms: 3.096817363 + -1.416666667 = 1.680150696
x = 1.680150696

Simplifying
x = 1.680150696

Subproblem 2
x + 1.416666667 = -3.096817363

Simplifying
x + 1.416666667 = -3.096817363

Reorder the terms:
1.416666667 + x = -3.096817363

Solving
1.416666667 + x = -3.096817363

Solving for variable 'x'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + x = -3.096817363 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + x = -3.096817363 + -1.416666667
x = -3.096817363 + -1.416666667

Combine like terms: -3.096817363 + -1.416666667 = -4.51348403
x = -4.51348403

Simplifying
x = -4.51348403

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.680150696, -4.51348403}