8x^4-28x^3=16x^2

Solution for 8x^4-28x^3=16x^2 equation:

Simplifying
8x4 + -28x3 = 16x2

Reorder the terms:
-28x3 + 8x4 = 16x2

Solving
-28x3 + 8x4 = 16x2

Solving for variable 'x'.

Reorder the terms:
-16x2 + -28x3 + 8x4 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-16x2 + -28x3 + 8x4 = 0

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-4 + -7x + 2x2) = 0

Factor a trinomial.
4x2((-1 + -2x)(4 + -1x)) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -0.5, 4}