Solve by Factoring 16x^2+2x-3=0

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

Step 1

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 $a \cdot c = 16 \cdot - 3 = - 48$ and whose sum is $b = 2$ .

Factor $2$ out of $2 x$ .

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

Rewrite $2$ as $- 6$ plus $8$

$16 x^{2} + (- 6 + 8) x - 3 = 0$

Apply the distributive property.

$16 x^{2} - 6 x + 8 x - 3 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(16 x^{2} - 6 x) + 8 x - 3 = 0$

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

$2 x (8 x - 3) + 1 (8 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $8 x - 3$ .

$(8 x - 3) (2 x + 1) = 0$

Step 2

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

$8 x - 3 = 0$

$2 x + 1 = 0$

Step 3

Set $8 x - 3$ equal to $0$ and solve for $x$ .

Set $8 x - 3$ equal to $0$ .

$8 x - 3 = 0$

Solve $8 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$8 x = 3$

Divide each term in $8 x = 3$ by $8$ and simplify.

Divide each term in $8 x = 3$ by $8$ .

$\frac{8 x}{8} = \frac{3}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{3}{8}$

Divide $x$ by $1$ .

$x = \frac{3}{8}$

Step 4

Set $2 x + 1$ equal to $0$ and solve for $x$ .

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Solve $2 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

The final solution is all the values that make $(8 x - 3) (2 x + 1) = 0$ true.

$x = \frac{3}{8}, - \frac{1}{2}$

Solve by Factoring 16x^2+2x-3=0

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