200x^4=-400x^3+12600x^2

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Solution for 200x^4=-400x^3+12600x^2 equation:


Simplifying
200x4 = -400x3 + 12600x2

Reorder the terms:
200x4 = 12600x2 + -400x3

Solving
200x4 = 12600x2 + -400x3

Solving for variable 'x'.

Reorder the terms:
-12600x2 + 400x3 + 200x4 = 12600x2 + -400x3 + -12600x2 + 400x3

Reorder the terms:
-12600x2 + 400x3 + 200x4 = 12600x2 + -12600x2 + -400x3 + 400x3

Combine like terms: 12600x2 + -12600x2 = 0
-12600x2 + 400x3 + 200x4 = 0 + -400x3 + 400x3
-12600x2 + 400x3 + 200x4 = -400x3 + 400x3

Combine like terms: -400x3 + 400x3 = 0
-12600x2 + 400x3 + 200x4 = 0

Factor out the Greatest Common Factor (GCF), '200x2'.
200x2(-63 + 2x + x2) = 0

Factor a trinomial.
200x2((-9 + -1x)(7 + -1x)) = 0

Ignore the factor 200.

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 '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 3

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {0, -9, 7}

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