10x^4-20x^3-30x^2=0

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Solution for 10x^4-20x^3-30x^2=0 equation:


Simplifying
10x4 + -20x3 + -30x2 = 0

Reorder the terms:
-30x2 + -20x3 + 10x4 = 0

Solving
-30x2 + -20x3 + 10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10x2'.
10x2(-3 + -2x + x2) = 0

Factor a trinomial.
10x2((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 10.

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 '(-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

Subproblem 3

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0, -1, 3}

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