3x^2+2x=-3x-2

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


Simplifying
3x2 + 2x = -3x + -2

Reorder the terms:
2x + 3x2 = -3x + -2

Reorder the terms:
2x + 3x2 = -2 + -3x

Solving
2x + 3x2 = -2 + -3x

Solving for variable 'x'.

Reorder the terms:
2 + 2x + 3x + 3x2 = -2 + -3x + 2 + 3x

Combine like terms: 2x + 3x = 5x
2 + 5x + 3x2 = -2 + -3x + 2 + 3x

Reorder the terms:
2 + 5x + 3x2 = -2 + 2 + -3x + 3x

Combine like terms: -2 + 2 = 0
2 + 5x + 3x2 = 0 + -3x + 3x
2 + 5x + 3x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
2 + 5x + 3x2 = 0

Factor a trinomial.
(1 + x)(2 + 3x) = 0


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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-1, -0.6666666667}

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