x^4+4x^3=5x^2

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Solution for x^4+4x^3=5x^2 equation:


Simplifying
x4 + 4x3 = 5x2

Reorder the terms:
4x3 + x4 = 5x2

Solving
4x3 + x4 = 5x2

Solving for variable 'x'.

Reorder the terms:
-5x2 + 4x3 + x4 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-5x2 + 4x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-5 + 4x + x2) = 0

Factor a trinomial.
x2((-5 + -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 '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

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, -5, 1}

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