Algebra Examples

$5 - 2 m - 3 m^{2} = 0$

Step 1

Factor the left side of the equation.

Tap for more steps...

Step 1.1

Factor $- 1$ out of $5 - 2 m - 3 m^{2}$ .

Tap for more steps...

Step 1.1.1

Reorder the expression.

Tap for more steps...

Step 1.1.1.1

Move $5$ .

$- 2 m - 3 m^{2} + 5 = 0$

Step 1.1.1.2

Reorder $- 2 m$ and $- 3 m^{2}$ .

$- 3 m^{2} - 2 m + 5 = 0$

Step 1.1.2

Factor $- 1$ out of $- 3 m^{2}$ .

$- (3 m^{2}) - 2 m + 5 = 0$

Step 1.1.3

Factor $- 1$ out of $- 2 m$ .

$- (3 m^{2}) - (2 m) + 5 = 0$

Step 1.1.4

Rewrite $5$ as $- 1 (- 5)$ .

$- (3 m^{2}) - (2 m) - 1 \cdot - 5 = 0$

Step 1.1.5

Factor $- 1$ out of $- (3 m^{2}) - (2 m)$ .

$- (3 m^{2} + 2 m) - 1 \cdot - 5 = 0$

Step 1.1.6

Factor $- 1$ out of $- (3 m^{2} + 2 m) - 1 (- 5)$ .

$- (3 m^{2} + 2 m - 5) = 0$

Step 1.2

Factor.

Tap for more steps...

Step 1.2.1

Factor by grouping.

Tap for more steps...

Step 1.2.1.1

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 $a \cdot c = 3 \cdot - 5 = - 15$ and whose sum is $b = 2$ .

Tap for more steps...

Step 1.2.1.1.1

Factor $2$ out of $2 m$ .

$- (3 m^{2} + 2 (m) - 5) = 0$

Step 1.2.1.1.2

Rewrite $2$ as $- 3$ plus $5$

$- (3 m^{2} + (- 3 + 5) m - 5) = 0$

Step 1.2.1.1.3

Apply the distributive property.

$- (3 m^{2} - 3 m + 5 m - 5) = 0$

Step 1.2.1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 1.2.1.2.1

Group the first two terms and the last two terms.

$- ((3 m^{2} - 3 m) + 5 m - 5) = 0$

Step 1.2.1.2.2

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

$- (3 m (m - 1) + 5 (m - 1)) = 0$

Step 1.2.1.3

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

$- ((m - 1) (3 m + 5)) = 0$

Step 1.2.2

Remove unnecessary parentheses.

$- (m - 1) (3 m + 5) = 0$

Step 2

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

$m - 1 = 0$

$3 m + 5 = 0$

Step 3

Set $m - 1$ equal to $0$ and solve for $m$ .

Tap for more steps...

Step 3.1

Set $m - 1$ equal to $0$ .

$m - 1 = 0$

Step 3.2

Add $1$ to both sides of the equation.

$m = 1$

Step 4

Set $3 m + 5$ equal to $0$ and solve for $m$ .

Tap for more steps...

Step 4.1

Set $3 m + 5$ equal to $0$ .

$3 m + 5 = 0$

Step 4.2

Solve $3 m + 5 = 0$ for $m$ .

Tap for more steps...

Step 4.2.1

Subtract $5$ from both sides of the equation.

$3 m = - 5$

Step 4.2.2

Divide each term in $3 m = - 5$ by $3$ and simplify.

Tap for more steps...

Step 4.2.2.1

Divide each term in $3 m = - 5$ by $3$ .

$\frac{3 m}{3} = \frac{- 5}{3}$

Step 4.2.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{3 m}{3} = \frac{- 5}{3}$

Step 4.2.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 5}{3}$

Step 4.2.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.2.3.1

Move the negative in front of the fraction.

$m = - \frac{5}{3}$

Step 5

The final solution is all the values that make $- (m - 1) (3 m + 5) = 0$ true.

$m = 1, - \frac{5}{3}$

Step 6