Solve for h 3h^2+17h=-10

$3 h^{2} + 17 h = - 10$

Step 1

Add $10$ to both sides of the equation.

$3 h^{2} + 17 h + 10 = 0$

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 $a \cdot c = 3 \cdot 10 = 30$ and whose sum is $b = 17$ .

Factor $17$ out of $17 h$ .

$3 h^{2} + 17 (h) + 10 = 0$

Rewrite $17$ as $2$ plus $15$

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

Apply the distributive property.

$3 h^{2} + 2 h + 15 h + 10 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$h (3 h + 2) + 5 (3 h + 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 h + 2$ .

$(3 h + 2) (h + 5) = 0$

Step 3

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

$3 h + 2 = 0$

$h + 5 = 0$

Step 4

Set $3 h + 2$ equal to $0$ and solve for $h$ .

Set $3 h + 2$ equal to $0$ .

$3 h + 2 = 0$

Solve $3 h + 2 = 0$ for $h$ .

Subtract $2$ from both sides of the equation.

$3 h = - 2$

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

Divide each term in $3 h = - 2$ by $3$ .

$\frac{3 h}{3} = \frac{- 2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 h}{3} = \frac{- 2}{3}$

Divide $h$ by $1$ .

$h = \frac{- 2}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$h = - \frac{2}{3}$

Step 5

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

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

$h + 5 = 0$

Subtract $5$ from both sides of the equation.

$h = - 5$

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$h = - 0.\overline{6}, - 5$

Solve for h 3h^2+17h=-10

Related Questions

Support LCMGCF.com by disabling your adblocker.