Solve for r 2r^2-7r-18=-3

$2 r^{2} - 7 r - 18 = - 3$

Step 1

Add $3$ to both sides of the equation.

$2 r^{2} - 7 r - 18 + 3 = 0$

Step 2

Add $- 18$ and $3$ .

$2 r^{2} - 7 r - 15 = 0$

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

Factor $- 7$ out of $- 7 r$ .

$2 r^{2} - 7 r - 15 = 0$

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 4

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

$2 r + 3 = 0$

$r - 5 = 0$

Step 5

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

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

$2 r + 3 = 0$

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

Subtract $3$ from both sides of the equation.

$2 r = - 3$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $r$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

Set $r - 5$ equal to $0$ and solve for $r$ .

Set $r - 5$ equal to $0$ .

$r - 5 = 0$

Add $5$ to both sides of the equation.

$r = 5$

Step 7

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

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$r = - 1.5, 5$

Mixed Number Form:

$r = - 1 \frac{1}{2}, 5$

Solve for r 2r^2-7r-18=-3

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