Solve by Factoring 3x^2-7x=x-4

$3 x^{2} - 7 x = x - 4$

Step 1

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

Subtract $x$ from both sides of the equation.

$3 x^{2} - 7 x - x = - 4$

Add $4$ to both sides of the equation.

$3 x^{2} - 7 x - x + 4 = 0$

Step 2

Subtract $x$ from $- 7 x$ .

$3 x^{2} - 8 x + 4 = 0$

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 $a \cdot c = 3 \cdot 4 = 12$ and whose sum is $b = - 8$ .

Factor $- 8$ out of $- 8 x$ .

$3 x^{2} - 8 x + 4 = 0$

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 4

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

$3 x - 2 = 0$

$x - 2 = 0$

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 $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 7

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

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

Solve by Factoring 3x^2-7x=x-4

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