0=4x^4-4x^3-168x^2

Solution for 0=4x^4-4x^3-168x^2 equation:

Simplifying
0 = 4x4 + -4x3 + -168x2

Reorder the terms:
0 = -168x2 + -4x3 + 4x4

Solving
0 = -168x2 + -4x3 + 4x4

Solving for variable 'x'.
Remove the zero:
168x2 + 4x3 + -4x4 = -168x2 + -4x3 + 4x4 + 168x2 + 4x3 + -4x4

Reorder the terms:
168x2 + 4x3 + -4x4 = -168x2 + 168x2 + -4x3 + 4x3 + 4x4 + -4x4

Combine like terms: -168x2 + 168x2 = 0
168x2 + 4x3 + -4x4 = 0 + -4x3 + 4x3 + 4x4 + -4x4
168x2 + 4x3 + -4x4 = -4x3 + 4x3 + 4x4 + -4x4

Combine like terms: -4x3 + 4x3 = 0
168x2 + 4x3 + -4x4 = 0 + 4x4 + -4x4
168x2 + 4x3 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
168x2 + 4x3 + -4x4 = 0

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(42 + x + -1x2) = 0

Factor a trinomial.
4x2((7 + -1x)(6 + 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {0, 7, -6}