-16x^2=x^4-10x^3

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Solution for -16x^2=x^4-10x^3 equation: 


Simplifying
-16x2 = x4 + -10x3

Reorder the terms:
-16x2 = -10x3 + x4

Solving
-16x2 = -10x3 + x4

Solving for variable 'x'.

Reorder the terms:
-16x2 + 10x3 + -1x4 = -10x3 + 10x3 + x4 + -1x4

Combine like terms: -10x3 + 10x3 = 0
-16x2 + 10x3 + -1x4 = 0 + x4 + -1x4
-16x2 + 10x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-16x2 + 10x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-16 + 10x + -1x2) = 0

Factor a trinomial.
x2((-8 + x)(2 + -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 + 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 8, 2}

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