3(2x-5)4x=10

Solution for 3(2x-5)4x=10 equation:

Simplifying
3(2x + -5) * 4x = 10

Reorder the terms:
3(-5 + 2x) * 4x = 10

Reorder the terms for easier multiplication:
3 * 4x(-5 + 2x) = 10

Multiply 3 * 4
12x(-5 + 2x) = 10
(-5 * 12x + 2x * 12x) = 10
(-60x + 24x2) = 10

Solving
-60x + 24x2 = 10

Solving for variable 'x'.

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

Combine like terms: 10 + -10 = 0
-10 + -60x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -30x + 12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -30x + 12x2)' equal to zero and attempt to solve:

Simplifying
-5 + -30x + 12x2 = 0

Solving
-5 + -30x + 12x2 = 0

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

Divide each side by '12'.
-0.4166666667 + -2.5x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -2.5x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -2.5x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -2.5x + x2 = 0 + 0.4166666667
-2.5x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
-2.5x + x2 = 0.4166666667

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 0.4166666667 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 0.4166666667 + 1.5625

Combine like terms: 0.4166666667 + 1.5625 = 1.9791666667
1.5625 + -2.5x + x2 = 1.9791666667

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 1.9791666667

Calculate the square root of the right side: 1.406828585

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.406828585 and -1.406828585.

Subproblem 1
x + -1.25 = 1.406828585

Simplifying
x + -1.25 = 1.406828585

Reorder the terms:
-1.25 + x = 1.406828585

Solving
-1.25 + x = 1.406828585

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 1.406828585 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.406828585 + 1.25
x = 1.406828585 + 1.25

Combine like terms: 1.406828585 + 1.25 = 2.656828585
x = 2.656828585

Simplifying
x = 2.656828585

Subproblem 2
x + -1.25 = -1.406828585

Simplifying
x + -1.25 = -1.406828585

Reorder the terms:
-1.25 + x = -1.406828585

Solving
-1.25 + x = -1.406828585

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -1.406828585 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.406828585 + 1.25
x = -1.406828585 + 1.25

Combine like terms: -1.406828585 + 1.25 = -0.156828585
x = -0.156828585

Simplifying
x = -0.156828585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.656828585, -0.156828585}
Solution
x = {2.656828585, -0.156828585}