Solve by Factoring 4x^2+21x=6x-14

$4 x^{2} + 21 x = 6 x - 14$

Step 1

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

Subtract $6 x$ from both sides of the equation.

$4 x^{2} + 21 x - 6 x = - 14$

Add $14$ to both sides of the equation.

$4 x^{2} + 21 x - 6 x + 14 = 0$

Step 2

Subtract $6 x$ from $21 x$ .

$4 x^{2} + 15 x + 14 = 0$

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 $a \cdot c = 4 \cdot 14 = 56$ and whose sum is $b = 15$ .

Factor $15$ out of $15 x$ .

$4 x^{2} + 15 (x) + 14 = 0$

Rewrite $15$ as $7$ plus $8$

$4 x^{2} + (7 + 8) x + 14 = 0$

Apply the distributive property.

$4 x^{2} + 7 x + 8 x + 14 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 7 x) + 8 x + 14 = 0$

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

$x (4 x + 7) + 2 (4 x + 7) = 0$

Factor the polynomial by factoring out the greatest common factor, $4 x + 7$ .

$(4 x + 7) (x + 2) = 0$

Step 4

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

$4 x + 7 = 0$

$x + 2 = 0$

Step 5

Set $4 x + 7$ equal to $0$ and solve for $x$ .

Set $4 x + 7$ equal to $0$ .

$4 x + 7 = 0$

Solve $4 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$4 x = - 7$

Divide each term in $4 x = - 7$ by $4$ and simplify.

Divide each term in $4 x = - 7$ by $4$ .

$\frac{4 x}{4} = \frac{- 7}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 7}{4}$

Divide $x$ by $1$ .

$x = \frac{- 7}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{4}$

Step 6

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

The final solution is all the values that make $(4 x + 7) (x + 2) = 0$ true.

$x = - \frac{7}{4}, - 2$

Solve by Factoring 4x^2+21x=6x-14

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