Solve by Factoring x(3x+16)=12

$x (3 x + 16) = 12$

Step 1

Subtract $12$ from both sides of the equation.

$x (3 x + 16) - 12 = 0$

Step 2

Simplify each term.

Apply the distributive property.

$x (3 x) + x \cdot 16 - 12 = 0$

Rewrite using the commutative property of multiplication.

$3 x \cdot x + x \cdot 16 - 12 = 0$

Move $16$ to the left of $x$ .

$3 x \cdot x + 16 \cdot x - 12 = 0$

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

Move $x$ .

$3 (x \cdot x) + 16 \cdot x - 12 = 0$

Multiply $x$ by $x$ .

$3 x^{2} + 16 \cdot x - 12 = 0$

$3 x^{2} + 16 x - 12 = 0$

Step 3

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 $a \cdot c = 3 \cdot - 12 = - 36$ and whose sum is $b = 16$ .

Factor $16$ out of $16 x$ .

$3 x^{2} + 16 (x) - 12 = 0$

Rewrite $16$ as $- 2$ plus $18$

$3 x^{2} + (- 2 + 18) x - 12 = 0$

Apply the distributive property.

$3 x^{2} - 2 x + 18 x - 12 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 2 x) + 18 x - 12 = 0$

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

$x (3 x - 2) + 6 (3 x - 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x - 2$ .

$(3 x - 2) (x + 6) = 0$

Step 4

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

$3 x - 2 = 0$

$x + 6 = 0$

Step 5

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 $x$ .

Add $2$ to 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 $1$ .

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

Step 6

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 7

The final solution is all the values that make $(3 x - 2) (x + 6) = 0$ true.

$x = \frac{2}{3}, - 6$

Solve by Factoring x(3x+16)=12

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