Solve for x (3x+3)(x+2)=2

$(3 x + 3) (x + 2) = 2$

Simplify $(3 x + 3) (x + 2)$ .

Expand $(3 x + 3) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$3 x (x + 2) + 3 (x + 2) = 2$

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 2 + 3 (x + 2) = 2$

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 2 + 3 x + 3 \cdot 2 = 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) + 3 x \cdot 2 + 3 x + 3 \cdot 2 = 2$

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot 2 + 3 x + 3 \cdot 2 = 2$

Multiply $2$ by $3$ .

$3 x^{2} + 6 x + 3 x + 3 \cdot 2 = 2$

Multiply $3$ by $2$ .

$3 x^{2} + 6 x + 3 x + 6 = 2$

Add $6 x$ and $3 x$ .

$3 x^{2} + 9 x + 6 = 2$

Move all terms to the left side of the equation and simplify.

Subtract $2$ from both sides of the equation.

$3 x^{2} + 9 x + 6 - 2 = 0$

Subtract $2$ from $6$ .

$3 x^{2} + 9 x + 4 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = 9$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (3 \cdot 4)}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raise $9$ to the power of $2$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 3 \cdot 4}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{- 9 \pm \sqrt{81 - 12 \cdot 4}}{2 \cdot 3}$

Multiply $- 12$ by $4$ .

$x = \frac{- 9 \pm \sqrt{81 - 48}}{2 \cdot 3}$

Subtract $48$ from $81$ .

$x = \frac{- 9 \pm \sqrt{33}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 9 \pm \sqrt{33}}{6}$

The final answer is the combination of both solutions.

$x = - \frac{9 - \sqrt{33}}{6}, - \frac{9 + \sqrt{33}}{6}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{9 - \sqrt{33}}{6}, - \frac{9 + \sqrt{33}}{6}$

Decimal Form:

$x = - 0.54257289 \dots, - 2.45742710 \dots$

Solve for x (3x+3)(x+2)=2

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