x^4+7x^3=8x^2

Solution for x^4+7x^3=8x^2 equation:

Simplifying
x4 + 7x3 = 8x2

Reorder the terms:
7x3 + x4 = 8x2

Solving
7x3 + x4 = 8x2

Solving for variable 'x'.

Reorder the terms:
-8x2 + 7x3 + x4 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-8x2 + 7x3 + x4 = 0

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

Factor a trinomial.
x2((-8 + -1x)(1 + -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 '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 3
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
Solution
x = {0, -8, 1}