Solve by Factoring 4x^2+7x=2

$4 x^{2} + 7 x = 2$

Step 1

Subtract $2$ from both sides of the equation.

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

Step 2

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 $a \cdot c = 4 \cdot - 2 = - 8$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

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

Rewrite $7$ as $- 1$ plus $8$

$4 x^{2} + (- 1 + 8) x - 2 = 0$

Apply the distributive property.

$4 x^{2} - 1 x + 8 x - 2 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 1 x) + 8 x - 2 = 0$

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

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

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

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

Step 3

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

$4 x - 1 = 0$

$x + 2 = 0$

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 $x$ .

Add $1$ to 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 $1$ .

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

Step 5

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 6

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

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

Solve by Factoring 4x^2+7x=2

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