3x^2=-6x-3

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Solution for 3x^2=-6x-3 equation:


Simplifying
3x2 = -6x + -3

Reorder the terms:
3x2 = -3 + -6x

Solving
3x2 = -3 + -6x

Solving for variable 'x'.

Reorder the terms:
3 + 6x + 3x2 = -3 + -6x + 3 + 6x

Reorder the terms:
3 + 6x + 3x2 = -3 + 3 + -6x + 6x

Combine like terms: -3 + 3 = 0
3 + 6x + 3x2 = 0 + -6x + 6x
3 + 6x + 3x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
3 + 6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 2x + x2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-1, -1}

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