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

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

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

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

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

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

Multiply (-3 + 2x) * (2 + 4x)
-3 + 5x = 16x + 2(-3(2 + 4x) + 2x * (2 + 4x))
-3 + 5x = 16x + 2((2 * -3 + 4x * -3) + 2x * (2 + 4x))
-3 + 5x = 16x + 2((-6 + -12x) + 2x * (2 + 4x))
-3 + 5x = 16x + 2(-6 + -12x + (2 * 2x + 4x * 2x))
-3 + 5x = 16x + 2(-6 + -12x + (4x + 8x2))

Combine like terms: -12x + 4x = -8x
-3 + 5x = 16x + 2(-6 + -8x + 8x2)
-3 + 5x = 16x + (-6 * 2 + -8x * 2 + 8x2 * 2)
-3 + 5x = 16x + (-12 + -16x + 16x2)

Reorder the terms:
-3 + 5x = -12 + 16x + -16x + 16x2

Combine like terms: 16x + -16x = 0
-3 + 5x = -12 + 0 + 16x2
-3 + 5x = -12 + 16x2

Solving
-3 + 5x = -12 + 16x2

Solving for variable 'x'.

Reorder the terms:
-3 + 12 + 5x + -16x2 = -12 + 16x2 + 12 + -16x2

Combine like terms: -3 + 12 = 9
9 + 5x + -16x2 = -12 + 16x2 + 12 + -16x2

Reorder the terms:
9 + 5x + -16x2 = -12 + 12 + 16x2 + -16x2

Combine like terms: -12 + 12 = 0
9 + 5x + -16x2 = 0 + 16x2 + -16x2
9 + 5x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
9 + 5x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.5625 + -0.3125x + x2 = 0

Move the constant term to the right:

Add '0.5625' to each side of the equation.
-0.5625 + -0.3125x + 0.5625 + x2 = 0 + 0.5625

Reorder the terms:
-0.5625 + 0.5625 + -0.3125x + x2 = 0 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + -0.3125x + x2 = 0 + 0.5625
-0.3125x + x2 = 0 + 0.5625

Combine like terms: 0 + 0.5625 = 0.5625
-0.3125x + x2 = 0.5625

The x term is -0.3125x.  Take half its coefficient (-0.15625).
Square it (0.0244140625) and add it to both sides.

Add '0.0244140625' to each side of the equation.
-0.3125x + 0.0244140625 + x2 = 0.5625 + 0.0244140625

Reorder the terms:
0.0244140625 + -0.3125x + x2 = 0.5625 + 0.0244140625

Combine like terms: 0.5625 + 0.0244140625 = 0.5869140625
0.0244140625 + -0.3125x + x2 = 0.5869140625

Factor a perfect square on the left side:
(x + -0.15625)(x + -0.15625) = 0.5869140625

Calculate the square root of the right side: 0.766103167

Break this problem into two subproblems by setting 
(x + -0.15625) equal to 0.766103167 and -0.766103167.

Subproblem 1
x + -0.15625 = 0.766103167

Simplifying
x + -0.15625 = 0.766103167

Reorder the terms:
-0.15625 + x = 0.766103167

Solving
-0.15625 + x = 0.766103167

Solving for variable 'x'.

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

Add '0.15625' to each side of the equation.
-0.15625 + 0.15625 + x = 0.766103167 + 0.15625

Combine like terms: -0.15625 + 0.15625 = 0.00000
0.00000 + x = 0.766103167 + 0.15625
x = 0.766103167 + 0.15625

Combine like terms: 0.766103167 + 0.15625 = 0.922353167
x = 0.922353167

Simplifying
x = 0.922353167

Subproblem 2
x + -0.15625 = -0.766103167

Simplifying
x + -0.15625 = -0.766103167

Reorder the terms:
-0.15625 + x = -0.766103167

Solving
-0.15625 + x = -0.766103167

Solving for variable 'x'.

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

Add '0.15625' to each side of the equation.
-0.15625 + 0.15625 + x = -0.766103167 + 0.15625

Combine like terms: -0.15625 + 0.15625 = 0.00000
0.00000 + x = -0.766103167 + 0.15625
x = -0.766103167 + 0.15625

Combine like terms: -0.766103167 + 0.15625 = -0.609853167
x = -0.609853167

Simplifying
x = -0.609853167

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.922353167, -0.609853167}