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

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

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

Reorder the terms:
5(-10 + 4x) + 10x = 4(2x + -3) * 2(x + -4)
(-10 * 5 + 4x * 5) + 10x = 4(2x + -3) * 2(x + -4)
(-50 + 20x) + 10x = 4(2x + -3) * 2(x + -4)

Combine like terms: 20x + 10x = 30x
-50 + 30x = 4(2x + -3) * 2(x + -4)

Reorder the terms:
-50 + 30x = 4(-3 + 2x) * 2(x + -4)

Reorder the terms:
-50 + 30x = 4(-3 + 2x) * 2(-4 + x)

Reorder the terms for easier multiplication:
-50 + 30x = 4 * 2(-3 + 2x)(-4 + x)

Multiply 4 * 2
-50 + 30x = 8(-3 + 2x)(-4 + x)

Multiply (-3 + 2x) * (-4 + x)
-50 + 30x = 8(-3(-4 + x) + 2x * (-4 + x))
-50 + 30x = 8((-4 * -3 + x * -3) + 2x * (-4 + x))
-50 + 30x = 8((12 + -3x) + 2x * (-4 + x))
-50 + 30x = 8(12 + -3x + (-4 * 2x + x * 2x))
-50 + 30x = 8(12 + -3x + (-8x + 2x2))

Combine like terms: -3x + -8x = -11x
-50 + 30x = 8(12 + -11x + 2x2)
-50 + 30x = (12 * 8 + -11x * 8 + 2x2 * 8)
-50 + 30x = (96 + -88x + 16x2)

Solving
-50 + 30x = 96 + -88x + 16x2

Solving for variable 'x'.

Reorder the terms:
-50 + -96 + 30x + 88x + -16x2 = 96 + -88x + 16x2 + -96 + 88x + -16x2

Combine like terms: -50 + -96 = -146
-146 + 30x + 88x + -16x2 = 96 + -88x + 16x2 + -96 + 88x + -16x2

Combine like terms: 30x + 88x = 118x
-146 + 118x + -16x2 = 96 + -88x + 16x2 + -96 + 88x + -16x2

Reorder the terms:
-146 + 118x + -16x2 = 96 + -96 + -88x + 88x + 16x2 + -16x2

Combine like terms: 96 + -96 = 0
-146 + 118x + -16x2 = 0 + -88x + 88x + 16x2 + -16x2
-146 + 118x + -16x2 = -88x + 88x + 16x2 + -16x2

Combine like terms: -88x + 88x = 0
-146 + 118x + -16x2 = 0 + 16x2 + -16x2
-146 + 118x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-146 + 118x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-73 + 59x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-73 + 59x + -8x2)' equal to zero and attempt to solve:

Simplifying
-73 + 59x + -8x2 = 0

Solving
-73 + 59x + -8x2 = 0

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

Divide each side by '-8'.
9.125 + -7.375x + x2 = 0

Move the constant term to the right:

Add '-9.125' to each side of the equation.
9.125 + -7.375x + -9.125 + x2 = 0 + -9.125

Reorder the terms:
9.125 + -9.125 + -7.375x + x2 = 0 + -9.125

Combine like terms: 9.125 + -9.125 = 0.000
0.000 + -7.375x + x2 = 0 + -9.125
-7.375x + x2 = 0 + -9.125

Combine like terms: 0 + -9.125 = -9.125
-7.375x + x2 = -9.125

The x term is -7.375x.  Take half its coefficient (-3.6875).
Square it (13.59765625) and add it to both sides.

Add '13.59765625' to each side of the equation.
-7.375x + 13.59765625 + x2 = -9.125 + 13.59765625

Reorder the terms:
13.59765625 + -7.375x + x2 = -9.125 + 13.59765625

Combine like terms: -9.125 + 13.59765625 = 4.47265625
13.59765625 + -7.375x + x2 = 4.47265625

Factor a perfect square on the left side:
(x + -3.6875)(x + -3.6875) = 4.47265625

Calculate the square root of the right side: 2.114865539

Break this problem into two subproblems by setting 
(x + -3.6875) equal to 2.114865539 and -2.114865539.

Subproblem 1
x + -3.6875 = 2.114865539

Simplifying
x + -3.6875 = 2.114865539

Reorder the terms:
-3.6875 + x = 2.114865539

Solving
-3.6875 + x = 2.114865539

Solving for variable 'x'.

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

Add '3.6875' to each side of the equation.
-3.6875 + 3.6875 + x = 2.114865539 + 3.6875

Combine like terms: -3.6875 + 3.6875 = 0.0000
0.0000 + x = 2.114865539 + 3.6875
x = 2.114865539 + 3.6875

Combine like terms: 2.114865539 + 3.6875 = 5.802365539
x = 5.802365539

Simplifying
x = 5.802365539

Subproblem 2
x + -3.6875 = -2.114865539

Simplifying
x + -3.6875 = -2.114865539

Reorder the terms:
-3.6875 + x = -2.114865539

Solving
-3.6875 + x = -2.114865539

Solving for variable 'x'.

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

Add '3.6875' to each side of the equation.
-3.6875 + 3.6875 + x = -2.114865539 + 3.6875

Combine like terms: -3.6875 + 3.6875 = 0.0000
0.0000 + x = -2.114865539 + 3.6875
x = -2.114865539 + 3.6875

Combine like terms: -2.114865539 + 3.6875 = 1.572634461
x = 1.572634461

Simplifying
x = 1.572634461

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.802365539, 1.572634461}
Solution
x = {5.802365539, 1.572634461}