7x^3=28x^2-28x

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Solution for 7x^3=28x^2-28x equation:


Simplifying
7x3 = 28x2 + -28x

Reorder the terms:
7x3 = -28x + 28x2

Solving
7x3 = -28x + 28x2

Solving for variable 'x'.

Reorder the terms:
28x + -28x2 + 7x3 = -28x + 28x2 + 28x + -28x2

Reorder the terms:
28x + -28x2 + 7x3 = -28x + 28x + 28x2 + -28x2

Combine like terms: -28x + 28x = 0
28x + -28x2 + 7x3 = 0 + 28x2 + -28x2
28x + -28x2 + 7x3 = 28x2 + -28x2

Combine like terms: 28x2 + -28x2 = 0
28x + -28x2 + 7x3 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(4 + -4x + x2) = 0

Factor a trinomial.
7x((2 + -1x)(2 + -1x)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

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

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, 2, 2}

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