-2(5x+3)=4x(x+16)

Solution for -2(5x+3)=4x(x+16) equation:

Simplifying
-2(5x + 3) = 4x(x + 16)

Reorder the terms:
-2(3 + 5x) = 4x(x + 16)
(3 * -2 + 5x * -2) = 4x(x + 16)
(-6 + -10x) = 4x(x + 16)

Reorder the terms:
-6 + -10x = 4x(16 + x)
-6 + -10x = (16 * 4x + x * 4x)
-6 + -10x = (64x + 4x2)

Solving
-6 + -10x = 64x + 4x2

Solving for variable 'x'.

Combine like terms: -10x + -64x = -74x
-6 + -74x + -4x2 = 64x + 4x2 + -64x + -4x2

Reorder the terms:
-6 + -74x + -4x2 = 64x + -64x + 4x2 + -4x2

Combine like terms: 64x + -64x = 0
-6 + -74x + -4x2 = 0 + 4x2 + -4x2
-6 + -74x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + -74x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 37x + 2x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 37x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + 37x + 2x2 = 0

Solving
3 + 37x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 18.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 18.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 18.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 18.5x + x2 = 0 + -1.5
18.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
18.5x + x2 = -1.5

The x term is 18.5x.  Take half its coefficient (9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
18.5x + 85.5625 + x2 = -1.5 + 85.5625

Reorder the terms:
85.5625 + 18.5x + x2 = -1.5 + 85.5625

Combine like terms: -1.5 + 85.5625 = 84.0625
85.5625 + 18.5x + x2 = 84.0625

Factor a perfect square on the left side:
(x + 9.25)(x + 9.25) = 84.0625

Calculate the square root of the right side: 9.16856041

Break this problem into two subproblems by setting 
(x + 9.25) equal to 9.16856041 and -9.16856041.

Subproblem 1
x + 9.25 = 9.16856041

Simplifying
x + 9.25 = 9.16856041

Reorder the terms:
9.25 + x = 9.16856041

Solving
9.25 + x = 9.16856041

Solving for variable 'x'.

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

Add '-9.25' to each side of the equation.
9.25 + -9.25 + x = 9.16856041 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + x = 9.16856041 + -9.25
x = 9.16856041 + -9.25

Combine like terms: 9.16856041 + -9.25 = -0.08143959
x = -0.08143959

Simplifying
x = -0.08143959

Subproblem 2
x + 9.25 = -9.16856041

Simplifying
x + 9.25 = -9.16856041

Reorder the terms:
9.25 + x = -9.16856041

Solving
9.25 + x = -9.16856041

Solving for variable 'x'.

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

Add '-9.25' to each side of the equation.
9.25 + -9.25 + x = -9.16856041 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + x = -9.16856041 + -9.25
x = -9.16856041 + -9.25

Combine like terms: -9.16856041 + -9.25 = -18.41856041
x = -18.41856041

Simplifying
x = -18.41856041

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.08143959, -18.41856041}
Solution
x = {-0.08143959, -18.41856041}