16x*16x-24=4x(4x-6)

Solution for 16x*16x-24=4x(4x-6) equation:

Simplifying
16x * 16x + -24 = 4x(4x + -6)

Reorder the terms for easier multiplication:
16 * 16x * x + -24 = 4x(4x + -6)

Multiply 16 * 16
256x * x + -24 = 4x(4x + -6)

Multiply x * x
256x2 + -24 = 4x(4x + -6)

Reorder the terms:
-24 + 256x2 = 4x(4x + -6)

Reorder the terms:
-24 + 256x2 = 4x(-6 + 4x)
-24 + 256x2 = (-6 * 4x + 4x * 4x)
-24 + 256x2 = (-24x + 16x2)

Solving
-24 + 256x2 = -24x + 16x2

Solving for variable 'x'.

Reorder the terms:
-24 + 24x + 256x2 + -16x2 = -24x + 16x2 + 24x + -16x2

Combine like terms: 256x2 + -16x2 = 240x2
-24 + 24x + 240x2 = -24x + 16x2 + 24x + -16x2

Reorder the terms:
-24 + 24x + 240x2 = -24x + 24x + 16x2 + -16x2

Combine like terms: -24x + 24x = 0
-24 + 24x + 240x2 = 0 + 16x2 + -16x2
-24 + 24x + 240x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-24 + 24x + 240x2 = 0

Factor out the Greatest Common Factor (GCF), '24'.
24(-1 + x + 10x2) = 0

Ignore the factor 24.
Subproblem 1
Set the factor '(-1 + x + 10x2)' equal to zero and attempt to solve:

Simplifying
-1 + x + 10x2 = 0

Solving
-1 + x + 10x2 = 0

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

Divide each side by '10'.
-0.1 + 0.1x + x2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.1x + 0.1 + x2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.1x + x2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.1x + x2 = 0.0 + 0.1
0.1x + x2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
0.1x + x2 = 0.1

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

Add '0.25' to each side of the equation.
0.1x + 0.25 + x2 = 0.1 + 0.25

Reorder the terms:
0.25 + 0.1x + x2 = 0.1 + 0.25

Combine like terms: 0.1 + 0.25 = 0.35
0.25 + 0.1x + x2 = 0.35

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.35

Calculate the square root of the right side: 0.591607978

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.591607978 and -0.591607978.

Subproblem 1
x + 0.5 = 0.591607978

Simplifying
x + 0.5 = 0.591607978

Reorder the terms:
0.5 + x = 0.591607978

Solving
0.5 + x = 0.591607978

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.591607978 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.591607978 + -0.5
x = 0.591607978 + -0.5

Combine like terms: 0.591607978 + -0.5 = 0.091607978
x = 0.091607978

Simplifying
x = 0.091607978

Subproblem 2
x + 0.5 = -0.591607978

Simplifying
x + 0.5 = -0.591607978

Reorder the terms:
0.5 + x = -0.591607978

Solving
0.5 + x = -0.591607978

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.591607978 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.591607978 + -0.5
x = -0.591607978 + -0.5

Combine like terms: -0.591607978 + -0.5 = -1.091607978
x = -1.091607978

Simplifying
x = -1.091607978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.091607978, -1.091607978}
Solution
x = {0.091607978, -1.091607978}