0=4x^4+4x^3-8x^2

Solution for 0=4x^4+4x^3-8x^2 equation:

Simplifying
0 = 4x4 + 4x3 + -8x2

Reorder the terms:
0 = -8x2 + 4x3 + 4x4

Solving
0 = -8x2 + 4x3 + 4x4

Solving for variable 'x'.
Remove the zero:
8x2 + -4x3 + -4x4 = -8x2 + 4x3 + 4x4 + 8x2 + -4x3 + -4x4

Reorder the terms:
8x2 + -4x3 + -4x4 = -8x2 + 8x2 + 4x3 + -4x3 + 4x4 + -4x4

Combine like terms: -8x2 + 8x2 = 0
8x2 + -4x3 + -4x4 = 0 + 4x3 + -4x3 + 4x4 + -4x4
8x2 + -4x3 + -4x4 = 4x3 + -4x3 + 4x4 + -4x4

Combine like terms: 4x3 + -4x3 = 0
8x2 + -4x3 + -4x4 = 0 + 4x4 + -4x4
8x2 + -4x3 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
8x2 + -4x3 + -4x4 = 0

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(2 + -1x + -1x2) = 0

Factor a trinomial.
4x2((1 + -1x)(2 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0, 1, -2}