x=(8x-3)(4x+5)

Solution for x=(8x-3)(4x+5) equation:

Simplifying
x = (8x + -3)(4x + 5)

Reorder the terms:
x = (-3 + 8x)(4x + 5)

Reorder the terms:
x = (-3 + 8x)(5 + 4x)

Multiply (-3 + 8x) * (5 + 4x)
x = (-3(5 + 4x) + 8x * (5 + 4x))
x = ((5 * -3 + 4x * -3) + 8x * (5 + 4x))
x = ((-15 + -12x) + 8x * (5 + 4x))
x = (-15 + -12x + (5 * 8x + 4x * 8x))
x = (-15 + -12x + (40x + 32x2))

Combine like terms: -12x + 40x = 28x
x = (-15 + 28x + 32x2)

Solving
x = -15 + 28x + 32x2

Solving for variable 'x'.

Reorder the terms:
15 + x + -28x + -32x2 = -15 + 28x + 32x2 + 15 + -28x + -32x2

Combine like terms: x + -28x = -27x
15 + -27x + -32x2 = -15 + 28x + 32x2 + 15 + -28x + -32x2

Reorder the terms:
15 + -27x + -32x2 = -15 + 15 + 28x + -28x + 32x2 + -32x2

Combine like terms: -15 + 15 = 0
15 + -27x + -32x2 = 0 + 28x + -28x + 32x2 + -32x2
15 + -27x + -32x2 = 28x + -28x + 32x2 + -32x2

Combine like terms: 28x + -28x = 0
15 + -27x + -32x2 = 0 + 32x2 + -32x2
15 + -27x + -32x2 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
15 + -27x + -32x2 = 0

Begin completing the square.  Divide all terms by
-32 the coefficient of the squared term: 

Divide each side by '-32'.
-0.46875 + 0.84375x + x2 = 0

Move the constant term to the right:

Add '0.46875' to each side of the equation.
-0.46875 + 0.84375x + 0.46875 + x2 = 0 + 0.46875

Reorder the terms:
-0.46875 + 0.46875 + 0.84375x + x2 = 0 + 0.46875

Combine like terms: -0.46875 + 0.46875 = 0.00000
0.00000 + 0.84375x + x2 = 0 + 0.46875
0.84375x + x2 = 0 + 0.46875

Combine like terms: 0 + 0.46875 = 0.46875
0.84375x + x2 = 0.46875

The x term is 0.84375x.  Take half its coefficient (0.421875).
Square it (0.1779785156) and add it to both sides.

Add '0.1779785156' to each side of the equation.
0.84375x + 0.1779785156 + x2 = 0.46875 + 0.1779785156

Reorder the terms:
0.1779785156 + 0.84375x + x2 = 0.46875 + 0.1779785156

Combine like terms: 0.46875 + 0.1779785156 = 0.6467285156
0.1779785156 + 0.84375x + x2 = 0.6467285156

Factor a perfect square on the left side:
(x + 0.421875)(x + 0.421875) = 0.6467285156

Calculate the square root of the right side: 0.804194327

Break this problem into two subproblems by setting 
(x + 0.421875) equal to 0.804194327 and -0.804194327.

Subproblem 1
x + 0.421875 = 0.804194327

Simplifying
x + 0.421875 = 0.804194327

Reorder the terms:
0.421875 + x = 0.804194327

Solving
0.421875 + x = 0.804194327

Solving for variable 'x'.

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

Add '-0.421875' to each side of the equation.
0.421875 + -0.421875 + x = 0.804194327 + -0.421875

Combine like terms: 0.421875 + -0.421875 = 0.000000
0.000000 + x = 0.804194327 + -0.421875
x = 0.804194327 + -0.421875

Combine like terms: 0.804194327 + -0.421875 = 0.382319327
x = 0.382319327

Simplifying
x = 0.382319327

Subproblem 2
x + 0.421875 = -0.804194327

Simplifying
x + 0.421875 = -0.804194327

Reorder the terms:
0.421875 + x = -0.804194327

Solving
0.421875 + x = -0.804194327

Solving for variable 'x'.

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

Add '-0.421875' to each side of the equation.
0.421875 + -0.421875 + x = -0.804194327 + -0.421875

Combine like terms: 0.421875 + -0.421875 = 0.000000
0.000000 + x = -0.804194327 + -0.421875
x = -0.804194327 + -0.421875

Combine like terms: -0.804194327 + -0.421875 = -1.226069327
x = -1.226069327

Simplifying
x = -1.226069327

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.382319327, -1.226069327}