Solve for x (3x+4)^2-3(x+2)=0

${(3 x + 4)}^{2} - 3 (x + 2) = 0$

Simplify each term.

Apply the distributive property.

${(3 x + 4)}^{2} - 3 x - 3 \cdot 2 = 0$

Multiply $- 3$ by $2$ .

${(3 x + 4)}^{2} - 3 x - 6 = 0$

Factor the left side of the equation.

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$9 u^{2} + 21 u + 10 = 0$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 9 \cdot 10 = 90$ and whose sum is $b = 21$ .

Factor $21$ out of $21 u$ .

$9 u^{2} + 21 (u) + 10 = 0$

Rewrite $21$ as $6$ plus $15$

$9 u^{2} + (6 + 15) u + 10 = 0$

Apply the distributive property.

$9 u^{2} + 6 u + 15 u + 10 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 u^{2} + 6 u) + 15 u + 10 = 0$

Factor out the greatest common factor (GCF) from each group.

$3 u (3 u + 2) + 5 (3 u + 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 u + 2$ .

$(3 u + 2) (3 u + 5) = 0$

Replace all occurrences of $u$ with $x$ .

$(3 x + 2) (3 x + 5) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$3 x + 2 = 0$

$3 x + 5 = 0$

Set $3 x + 2$ equal to $0$ and solve for $x$ .

Set $3 x + 2$ equal to $0$ .

$3 x + 2 = 0$

Solve $3 x + 2 = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$3 x = - 2$

Divide each term in $3 x = - 2$ by $3$ and simplify.

Divide each term in $3 x = - 2$ by $3$ .

$\frac{3 x}{3} = \frac{- 2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 2}{3}$

Divide $x$ by $1$ .

$x = \frac{- 2}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Set $3 x + 5$ equal to $0$ and solve for $x$ .

Set $3 x + 5$ equal to $0$ .

$3 x + 5 = 0$

Solve $3 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$3 x = - 5$

Divide each term in $3 x = - 5$ by $3$ and simplify.

Divide each term in $3 x = - 5$ by $3$ .

$\frac{3 x}{3} = \frac{- 5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 5}{3}$

Divide $x$ by $1$ .

$x = \frac{- 5}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{3}$

The final solution is all the values that make $(3 x + 2) (3 x + 5) = 0$ true.

$x = - \frac{2}{3}, - \frac{5}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{3}, - \frac{5}{3}$

Decimal Form:

$x = - 0.\overline{6}, - 1.\overline{6}$

Mixed Number Form:

$x = - \frac{2}{3}, - 1 \frac{2}{3}$

Solve for x (3x+4)^2-3(x+2)=0

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