2X^4+26X^3+80X^2=

Solution for 2X^4+26X^3+80X^2= equation:

Simplifying
2X4 + 26X3 + 80X2 = 0

Reorder the terms:
80X2 + 26X3 + 2X4 = 0

Solving
80X2 + 26X3 + 2X4 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2X2'.
2X2(40 + 13X + X2) = 0

Factor a trinomial.
2X2((8 + X)(5 + X)) = 0

Ignore the factor 2.
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 '(8 + X)' equal to zero and attempt to solve:

Simplifying
8 + X = 0

Solving
8 + X = 0

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

Add '-8' to each side of the equation.
8 + -8 + X = 0 + -8

Combine like terms: 8 + -8 = 0
0 + X = 0 + -8
X = 0 + -8

Combine like terms: 0 + -8 = -8
X = -8

Simplifying
X = -8
Subproblem 3
Set the factor '(5 + X)' equal to zero and attempt to solve:

Simplifying
5 + X = 0

Solving
5 + X = 0

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

Add '-5' to each side of the equation.
5 + -5 + X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + X = 0 + -5
X = 0 + -5

Combine like terms: 0 + -5 = -5
X = -5

Simplifying
X = -5
Solution
X = {0, -8, -5}