Solve by Factoring 2z^2+7z-15=0

$2 z^{2} + 7 z - 15 = 0$

Step 1

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 $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = 7$ .

Factor $7$ out of $7 z$ .

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

Rewrite $7$ as $- 3$ plus $10$

$2 z^{2} + (- 3 + 10) z - 15 = 0$

Apply the distributive property.

$2 z^{2} - 3 z + 10 z - 15 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 z^{2} - 3 z) + 10 z - 15 = 0$

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

$z (2 z - 3) + 5 (2 z - 3) = 0$

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

$(2 z - 3) (z + 5) = 0$

Step 2

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

$2 z - 3 = 0$

$z + 5 = 0$

Step 3

Set $2 z - 3$ equal to $0$ and solve for $z$ .

Set $2 z - 3$ equal to $0$ .

$2 z - 3 = 0$

Solve $2 z - 3 = 0$ for $z$ .

Add $3$ to both sides of the equation.

$2 z = 3$

Divide each term in $2 z = 3$ by $2$ and simplify.

Divide each term in $2 z = 3$ by $2$ .

$\frac{2 z}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 z}{2} = \frac{3}{2}$

Divide $z$ by $1$ .

$z = \frac{3}{2}$

Step 4

Set $z + 5$ equal to $0$ and solve for $z$ .

Set $z + 5$ equal to $0$ .

$z + 5 = 0$

Subtract $5$ from both sides of the equation.

$z = - 5$

Step 5

The final solution is all the values that make $(2 z - 3) (z + 5) = 0$ true.

$z = \frac{3}{2}, - 5$

Solve by Factoring 2z^2+7z-15=0

Related Questions

Support LCMGCF.com by disabling your adblocker.