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

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

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

Reorder the terms:
5(4 + 3x) = 10x(x + 2)
(4 * 5 + 3x * 5) = 10x(x + 2)
(20 + 15x) = 10x(x + 2)

Reorder the terms:
20 + 15x = 10x(2 + x)
20 + 15x = (2 * 10x + x * 10x)
20 + 15x = (20x + 10x2)

Solving
20 + 15x = 20x + 10x2

Solving for variable 'x'.

Combine like terms: 15x + -20x = -5x
20 + -5x + -10x2 = 20x + 10x2 + -20x + -10x2

Reorder the terms:
20 + -5x + -10x2 = 20x + -20x + 10x2 + -10x2

Combine like terms: 20x + -20x = 0
20 + -5x + -10x2 = 0 + 10x2 + -10x2
20 + -5x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
20 + -5x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -1x + -2x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(4 + -1x + -2x2)' equal to zero and attempt to solve:

Simplifying
4 + -1x + -2x2 = 0

Solving
4 + -1x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-2 + 0.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.5x + x2 = 0 + 2
0.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.5x + x2 = 2

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 2 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + 0.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
x + 0.25 = 1.436140662

Simplifying
x + 0.25 = 1.436140662

Reorder the terms:
0.25 + x = 1.436140662

Solving
0.25 + x = 1.436140662

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.436140662 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.436140662 + -0.25
x = 1.436140662 + -0.25

Combine like terms: 1.436140662 + -0.25 = 1.186140662
x = 1.186140662

Simplifying
x = 1.186140662

Subproblem 2
x + 0.25 = -1.436140662

Simplifying
x + 0.25 = -1.436140662

Reorder the terms:
0.25 + x = -1.436140662

Solving
0.25 + x = -1.436140662

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.436140662 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.436140662 + -0.25
x = -1.436140662 + -0.25

Combine like terms: -1.436140662 + -0.25 = -1.686140662
x = -1.686140662

Simplifying
x = -1.686140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.186140662, -1.686140662}
Solution
x = {1.186140662, -1.686140662}