3(2x-5)4x=2(x+5)

Solution for 3(2x-5)4x=2(x+5) equation:

Simplifying
3(2x + -5) * 4x = 2(x + 5)

Reorder the terms:
3(-5 + 2x) * 4x = 2(x + 5)

Reorder the terms for easier multiplication:
3 * 4x(-5 + 2x) = 2(x + 5)

Multiply 3 * 4
12x(-5 + 2x) = 2(x + 5)
(-5 * 12x + 2x * 12x) = 2(x + 5)
(-60x + 24x2) = 2(x + 5)

Reorder the terms:
-60x + 24x2 = 2(5 + x)
-60x + 24x2 = (5 * 2 + x * 2)
-60x + 24x2 = (10 + 2x)

Solving
-60x + 24x2 = 10 + 2x

Solving for variable 'x'.

Reorder the terms:
-10 + -60x + -2x + 24x2 = 10 + 2x + -10 + -2x

Combine like terms: -60x + -2x = -62x
-10 + -62x + 24x2 = 10 + 2x + -10 + -2x

Reorder the terms:
-10 + -62x + 24x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
-10 + -62x + 24x2 = 0 + 2x + -2x
-10 + -62x + 24x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-10 + -62x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -31x + 12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -31x + 12x2)' equal to zero and attempt to solve:

Simplifying
-5 + -31x + 12x2 = 0

Solving
-5 + -31x + 12x2 = 0

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

Divide each side by '12'.
-0.4166666667 + -2.583333333x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -2.583333333x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -2.583333333x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -2.583333333x + x2 = 0 + 0.4166666667
-2.583333333x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
-2.583333333x + x2 = 0.4166666667

The x term is -2.583333333x.  Take half its coefficient (-1.291666667).
Square it (1.668402779) and add it to both sides.

Add '1.668402779' to each side of the equation.
-2.583333333x + 1.668402779 + x2 = 0.4166666667 + 1.668402779

Reorder the terms:
1.668402779 + -2.583333333x + x2 = 0.4166666667 + 1.668402779

Combine like terms: 0.4166666667 + 1.668402779 = 2.0850694457
1.668402779 + -2.583333333x + x2 = 2.0850694457

Factor a perfect square on the left side:
(x + -1.291666667)(x + -1.291666667) = 2.0850694457

Calculate the square root of the right side: 1.443976955

Break this problem into two subproblems by setting 
(x + -1.291666667) equal to 1.443976955 and -1.443976955.

Subproblem 1
x + -1.291666667 = 1.443976955

Simplifying
x + -1.291666667 = 1.443976955

Reorder the terms:
-1.291666667 + x = 1.443976955

Solving
-1.291666667 + x = 1.443976955

Solving for variable 'x'.

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

Add '1.291666667' to each side of the equation.
-1.291666667 + 1.291666667 + x = 1.443976955 + 1.291666667

Combine like terms: -1.291666667 + 1.291666667 = 0.000000000
0.000000000 + x = 1.443976955 + 1.291666667
x = 1.443976955 + 1.291666667

Combine like terms: 1.443976955 + 1.291666667 = 2.735643622
x = 2.735643622

Simplifying
x = 2.735643622

Subproblem 2
x + -1.291666667 = -1.443976955

Simplifying
x + -1.291666667 = -1.443976955

Reorder the terms:
-1.291666667 + x = -1.443976955

Solving
-1.291666667 + x = -1.443976955

Solving for variable 'x'.

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

Add '1.291666667' to each side of the equation.
-1.291666667 + 1.291666667 + x = -1.443976955 + 1.291666667

Combine like terms: -1.291666667 + 1.291666667 = 0.000000000
0.000000000 + x = -1.443976955 + 1.291666667
x = -1.443976955 + 1.291666667

Combine like terms: -1.443976955 + 1.291666667 = -0.152310288
x = -0.152310288

Simplifying
x = -0.152310288

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.735643622, -0.152310288}
Solution
x = {2.735643622, -0.152310288}