(2x^2)(8x+2)-(4x)(4x^2+2x+1)=0

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Solution for (2x^2)(8x+2)-(4x)(4x^2+2x+1)=0 equation: 


Simplifying
(2x2)(8x + 2) + -1(4x)(4x2 + 2x + 1) = 0

Remove parenthesis around (2x2)
2x2(8x + 2) + -1(4x)(4x2 + 2x + 1) = 0

Reorder the terms:
2x2(2 + 8x) + -1(4x)(4x2 + 2x + 1) = 0
(2 * 2x2 + 8x * 2x2) + -1(4x)(4x2 + 2x + 1) = 0
(4x2 + 16x3) + -1(4x)(4x2 + 2x + 1) = 0

Remove parenthesis around (4x)
4x2 + 16x3 + -1 * 4x(4x2 + 2x + 1) = 0

Reorder the terms:
4x2 + 16x3 + -1 * 4x(1 + 2x + 4x2) = 0

Multiply -1 * 4
4x2 + 16x3 + -4x(1 + 2x + 4x2) = 0
4x2 + 16x3 + (1 * -4x + 2x * -4x + 4x2 * -4x) = 0
4x2 + 16x3 + (-4x + -8x2 + -16x3) = 0

Reorder the terms:
-4x + 4x2 + -8x2 + 16x3 + -16x3 = 0

Combine like terms: 4x2 + -8x2 = -4x2
-4x + -4x2 + 16x3 + -16x3 = 0

Combine like terms: 16x3 + -16x3 = 0
-4x + -4x2 + 0 = 0
-4x + -4x2 = 0

Solving
-4x + -4x2 = 0

Solving for variable 'x'.

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

Ignore the factor -4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {0, -1}

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