Basic Math Examples

4 v^{2} = - 5 v + 6

$4 v^{2} = - 5 v + 6$

Step 1

Add

5 v

$5 v$ to both sides of the equation.

4 v^{2} + 5 v = 6

$4 v^{2} + 5 v = 6$

Step 2

Subtract

6

$6$ from both sides of the equation.

4 v^{2} + 5 v - 6 = 0

$4 v^{2} + 5 v - 6 = 0$

Step 3

Factor by grouping.

Tap for more steps...

Step 3.1

For a polynomial of the form

a x^{2} + b x + c

$a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is

a \cdot c = 4 \cdot - 6 = - 24

$a \cdot c = 4 \cdot - 6 = - 24$ and whose sum is

b = 5

$b = 5$ .

Tap for more steps...

Step 3.1.1

Factor

5

$5$ out of

5 v

$5 v$ .

4 v^{2} + 5 (v) - 6 = 0

$4 v^{2} + 5 (v) - 6 = 0$

Step 3.1.2

Rewrite

5

$5$ as

- 3

$- 3$ plus

8

$8$

4 v^{2} + (- 3 + 8) v - 6 = 0

$4 v^{2} + (- 3 + 8) v - 6 = 0$

Step 3.1.3

Apply the distributive property.

4 v^{2} - 3 v + 8 v - 6 = 0

$4 v^{2} - 3 v + 8 v - 6 = 0$

4 v^{2} - 3 v + 8 v - 6 = 0

$4 v^{2} - 3 v + 8 v - 6 = 0$

Step 3.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 3.2.1

Group the first two terms and the last two terms.

(4 v^{2} - 3 v) + 8 v - 6 = 0

$(4 v^{2} - 3 v) + 8 v - 6 = 0$

Step 3.2.2

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

v (4 v - 3) + 2 (4 v - 3) = 0

$v (4 v - 3) + 2 (4 v - 3) = 0$

v (4 v - 3) + 2 (4 v - 3) = 0

$v (4 v - 3) + 2 (4 v - 3) = 0$

Step 3.3

Factor the polynomial by factoring out the greatest common factor,

4 v - 3

$4 v - 3$ .

(4 v - 3) (v + 2) = 0

$(4 v - 3) (v + 2) = 0$

(4 v - 3) (v + 2) = 0

$(4 v - 3) (v + 2) = 0$

Step 4

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

4 v - 3 = 0

$4 v - 3 = 0$

v + 2 = 0

$v + 2 = 0$

Step 5

Set

4 v - 3

$4 v - 3$ equal to

0

$0$ and solve for

v

$v$ .

Tap for more steps...

Step 5.1

Set

4 v - 3

$4 v - 3$ equal to

0

$0$ .

4 v - 3 = 0

$4 v - 3 = 0$

Step 5.2

Solve

4 v - 3 = 0

$4 v - 3 = 0$ for

v

$v$ .

Tap for more steps...

Step 5.2.1

Add

3

$3$ to both sides of the equation.

4 v = 3

$4 v = 3$

Step 5.2.2

Divide each term in

4 v = 3

$4 v = 3$ by

4

$4$ and simplify.

Tap for more steps...

Step 5.2.2.1

Divide each term in

4 v = 3

$4 v = 3$ by

4

$4$ .

\frac{4 v}{4} = \frac{3}{4}

$\frac{4 v}{4} = \frac{3}{4}$

Step 5.2.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.2.1

Cancel the common factor of

4

$4$ .

Tap for more steps...

Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{4 v}{4} = \frac{3}{4}$

Step 5.2.2.2.1.2

Divide

$v$ by

$1$ .

$v = \frac{3}{4}$

Step 6

Set

$v + 2$ equal to

$0$ and solve for

$v$ .

Tap for more steps...

Step 6.1

Set

$v + 2$ equal to

$0$ .

$v + 2 = 0$

Step 6.2

Subtract

$2$ from both sides of the equation.

$v = - 2$

Step 7

The final solution is all the values that make

$(4 v - 3) (v + 2) = 0$ true.

$v = \frac{3}{4}, - 2$

Step 8

The result can be shown in multiple forms.

Exact Form:

$v = \frac{3}{4}, - 2$

Decimal Form:

$v = 0.75, - 2$