Solve by Factoring 21x^2-6=15x

$21 x^{2} - 6 = 15 x$

Step 1

Subtract $15 x$ from both sides of the equation.

$21 x^{2} - 6 - 15 x = 0$

Step 2

Factor $3$ out of $21 x^{2} - 6 - 15 x$ .

Factor $3$ out of $21 x^{2}$ .

$3 (7 x^{2}) - 6 - 15 x = 0$

Factor $3$ out of $- 6$ .

$3 (7 x^{2}) + 3 (- 2) - 15 x = 0$

Factor $3$ out of $- 15 x$ .

$3 (7 x^{2}) + 3 (- 2) + 3 (- 5 x) = 0$

Factor $3$ out of $3 (7 x^{2}) + 3 (- 2)$ .

$3 (7 x^{2} - 2) + 3 (- 5 x) = 0$

Factor $3$ out of $3 (7 x^{2} - 2) + 3 (- 5 x)$ .

$3 (7 x^{2} - 2 - 5 x) = 0$

Step 3

Factor.

Factor by grouping.

Reorder terms.

$3 (7 x^{2} - 5 x - 2) = 0$

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 $a \cdot c = 7 \cdot - 2 = - 14$ and whose sum is $b = - 5$ .

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

$3 (7 x^{2} - 5 x - 2) = 0$

Rewrite $- 5$ as $2$ plus $- 7$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 (x (7 x + 2) - (7 x + 2)) = 0$

Factor the polynomial by factoring out the greatest common factor, $7 x + 2$ .

$3 ((7 x + 2) (x - 1)) = 0$

Remove unnecessary parentheses.

$3 (7 x + 2) (x - 1) = 0$

Step 4

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

$7 x + 2 = 0$

$x - 1 = 0$

Step 5

Set $7 x + 2$ equal to $0$ and solve for $x$ .

Set $7 x + 2$ equal to $0$ .

$7 x + 2 = 0$

Solve $7 x + 2 = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$7 x = - 2$

Divide each term in $7 x = - 2$ by $7$ and simplify.

Divide each term in $7 x = - 2$ by $7$ .

$\frac{7 x}{7} = \frac{- 2}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 2}{7}$

Divide $x$ by $1$ .

$x = \frac{- 2}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{7}$

Step 6

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 7

The final solution is all the values that make $3 (7 x + 2) (x - 1) = 0$ true.

$x = - \frac{2}{7}, 1$

Solve by Factoring 21x^2-6=15x

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