(3x^2+2)+(x^3+3x^2-2)=

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Solution for (3x^2+2)+(x^3+3x^2-2)= equation:


Simplifying
(3x2 + 2) + (x3 + 3x2 + -2) = 0

Reorder the terms:
(2 + 3x2) + (x3 + 3x2 + -2) = 0

Remove parenthesis around (2 + 3x2)
2 + 3x2 + (x3 + 3x2 + -2) = 0

Reorder the terms:
2 + 3x2 + (-2 + 3x2 + x3) = 0

Remove parenthesis around (-2 + 3x2 + x3)
2 + 3x2 + -2 + 3x2 + x3 = 0

Reorder the terms:
2 + -2 + 3x2 + 3x2 + x3 = 0

Combine like terms: 2 + -2 = 0
0 + 3x2 + 3x2 + x3 = 0
3x2 + 3x2 + x3 = 0

Combine like terms: 3x2 + 3x2 = 6x2
6x2 + x3 = 0

Solving
6x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6 + x) = 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Solution

x = {0, -6}

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