Solve by Factoring 12x^2-2=5x

$12 x^{2} - 2 = 5 x$

Step 1

Subtract $5 x$ from both sides of the equation.

$12 x^{2} - 2 - 5 x = 0$

Step 2

Factor by grouping.

Reorder terms.

$12 x^{2} - 5 x - 2 = 0$

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 $a \cdot c = 12 \cdot - 2 = - 24$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 x$ .

$12 x^{2} - 5 x - 2 = 0$

Rewrite $- 5$ as $3$ plus $- 8$

$12 x^{2} + (3 - 8) x - 2 = 0$

Apply the distributive property.

$12 x^{2} + 3 x - 8 x - 2 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} + 3 x) - 8 x - 2 = 0$

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

$3 x (4 x + 1) - 2 (4 x + 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$(4 x + 1) (3 x - 2) = 0$

Step 3

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

$4 x + 1 = 0$

$3 x - 2 = 0$

Step 4

Set $4 x + 1$ equal to $0$ and solve for $x$ .

Set $4 x + 1$ equal to $0$ .

$4 x + 1 = 0$

Solve $4 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$4 x = - 1$

Divide each term in $4 x = - 1$ by $4$ and simplify.

Divide each term in $4 x = - 1$ by $4$ .

$\frac{4 x}{4} = \frac{- 1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 1}{4}$

Divide $x$ by $1$ .

$x = \frac{- 1}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{4}$

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

The final solution is all the values that make $(4 x + 1) (3 x - 2) = 0$ true.

$x = - \frac{1}{4}, \frac{2}{3}$

Solve by Factoring 12x^2-2=5x

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