3(x-4)4(x+5)=10

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

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

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

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

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

Multiply 3 * 4
12(-4 + x)(5 + x) = 10

Multiply (-4 + x) * (5 + x)
12(-4(5 + x) + x(5 + x)) = 10
12((5 * -4 + x * -4) + x(5 + x)) = 10
12((-20 + -4x) + x(5 + x)) = 10
12(-20 + -4x + (5 * x + x * x)) = 10
12(-20 + -4x + (5x + x2)) = 10

Combine like terms: -4x + 5x = 1x
12(-20 + 1x + x2) = 10
(-20 * 12 + 1x * 12 + x2 * 12) = 10
(-240 + 12x + 12x2) = 10

Solving
-240 + 12x + 12x2 = 10

Solving for variable 'x'.

Reorder the terms:
-240 + -10 + 12x + 12x2 = 10 + -10

Combine like terms: -240 + -10 = -250
-250 + 12x + 12x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-250 + 12x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 6x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-125 + 6x + 6x2)' equal to zero and attempt to solve:

Simplifying
-125 + 6x + 6x2 = 0

Solving
-125 + 6x + 6x2 = 0

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

Divide each side by '6'.
-20.83333333 + x + x2 = 0

Move the constant term to the right:

Add '20.83333333' to each side of the equation.
-20.83333333 + x + 20.83333333 + x2 = 0 + 20.83333333

Reorder the terms:
-20.83333333 + 20.83333333 + x + x2 = 0 + 20.83333333

Combine like terms: -20.83333333 + 20.83333333 = 0.00000000
0.00000000 + x + x2 = 0 + 20.83333333
x + x2 = 0 + 20.83333333

Combine like terms: 0 + 20.83333333 = 20.83333333
x + x2 = 20.83333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 20.83333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 20.83333333 + 0.25

Combine like terms: 20.83333333 + 0.25 = 21.08333333
1.25 + x2 = 21.08333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 21.08333333

Calculate the square root of the right side: 4.591659104

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.591659104 and -4.591659104.

Subproblem 1
x + 0.5 = 4.591659104

Simplifying
x + 0.5 = 4.591659104

Reorder the terms:
0.5 + x = 4.591659104

Solving
0.5 + x = 4.591659104

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.591659104 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.591659104 + -0.5
x = 4.591659104 + -0.5

Combine like terms: 4.591659104 + -0.5 = 4.091659104
x = 4.091659104

Simplifying
x = 4.091659104

Subproblem 2
x + 0.5 = -4.591659104

Simplifying
x + 0.5 = -4.591659104

Reorder the terms:
0.5 + x = -4.591659104

Solving
0.5 + x = -4.591659104

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.591659104 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.591659104 + -0.5
x = -4.591659104 + -0.5

Combine like terms: -4.591659104 + -0.5 = -5.091659104
x = -5.091659104

Simplifying
x = -5.091659104

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.091659104, -5.091659104}
Solution
x = {4.091659104, -5.091659104}