Solve by Factoring 3x^2=16x+12

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

Step 1

Move all the expressions to the left side of the equation.

Subtract $16 x$ from both sides of the equation.

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

Subtract $12$ from both sides of the equation.

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

Step 2

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 3

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 4

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.

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

Step 5

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

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

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Step 6

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

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

Solve by Factoring 3x^2=16x+12

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