5x^3+35x^2+45x=5x^2

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Solution for 5x^3+35x^2+45x=5x^2 equation:


Simplifying
5x3 + 35x2 + 45x = 5x2

Reorder the terms:
45x + 35x2 + 5x3 = 5x2

Solving
45x + 35x2 + 5x3 = 5x2

Solving for variable 'x'.

Reorder the terms:
45x + 35x2 + -5x2 + 5x3 = 5x2 + -5x2

Combine like terms: 35x2 + -5x2 = 30x2
45x + 30x2 + 5x3 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
45x + 30x2 + 5x3 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(9 + 6x + x2) = 0

Factor a trinomial.
5x((3 + x)(3 + x)) = 0

Ignore the factor 5.

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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 3

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {0, -3, -3}

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