x^4-10x^3=-24x^2

Solution for x^4-10x^3=-24x^2 equation:

Simplifying
x4 + -10x3 = -24x2

Reorder the terms:
-10x3 + x4 = -24x2

Solving
-10x3 + x4 = -24x2

Solving for variable 'x'.

Reorder the terms:
24x2 + -10x3 + x4 = -24x2 + 24x2

Combine like terms: -24x2 + 24x2 = 0
24x2 + -10x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(24 + -10x + x2) = 0

Factor a trinomial.
x2((4 + -1x)(6 + -1x)) = 0

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 '(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
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 4, 6}