8x^4-48x^3=56x^2

Solution for 8x^4-48x^3=56x^2 equation:

Simplifying
8x4 + -48x3 = 56x2

Reorder the terms:
-48x3 + 8x4 = 56x2

Solving
-48x3 + 8x4 = 56x2

Solving for variable 'x'.

Reorder the terms:
-56x2 + -48x3 + 8x4 = 56x2 + -56x2

Combine like terms: 56x2 + -56x2 = 0
-56x2 + -48x3 + 8x4 = 0

Factor out the Greatest Common Factor (GCF), '8x2'.
8x2(-7 + -6x + x2) = 0

Factor a trinomial.
8x2((-1 + -1x)(7 + -1x)) = 0

Ignore the factor 8.
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 '(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
Solution
x = {0, -1, 7}