Finite Math Examples

$96 x^{2} - 120 x + 24 = 0$

Step 1

Factor the left side of the equation.

Tap for more steps...

Step 1.1

Factor $24$ out of $96 x^{2} - 120 x + 24$ .

Tap for more steps...

Step 1.1.1

Factor $24$ out of $96 x^{2}$ .

$24 (4 x^{2}) - 120 x + 24 = 0$

Step 1.1.2

Factor $24$ out of $- 120 x$ .

$24 (4 x^{2}) + 24 (- 5 x) + 24 = 0$

Step 1.1.3

Factor $24$ out of $24$ .

$24 (4 x^{2}) + 24 (- 5 x) + 24 (1) = 0$

Step 1.1.4

Factor $24$ out of $24 (4 x^{2}) + 24 (- 5 x)$ .

$24 (4 x^{2} - 5 x) + 24 (1) = 0$

Step 1.1.5

Factor $24$ out of $24 (4 x^{2} - 5 x) + 24 (1)$ .

$24 (4 x^{2} - 5 x + 1) = 0$

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 $a \cdot c = 4 \cdot 1 = 4$ and whose sum is $b = - 5$ .

Tap for more steps...

Step 1.2.1.1.1

Factor $- 5$ out of $- 5 x$ .

$24 (4 x^{2} - 5 x + 1) = 0$

Step 1.2.1.1.2

Rewrite $- 5$ as $- 1$ plus $- 4$

$24 (4 x^{2} + (- 1 - 4) x + 1) = 0$

Step 1.2.1.1.3

Apply the distributive property.

$24 (4 x^{2} - 1 x - 4 x + 1) = 0$

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.

$24 ((4 x^{2} - 1 x) - 4 x + 1) = 0$

Step 1.2.1.2.2

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

$24 (x (4 x - 1) - (4 x - 1)) = 0$

Step 1.2.1.3

Factor the polynomial by factoring out the greatest common factor, $4 x - 1$ .

$24 ((4 x - 1) (x - 1)) = 0$

Step 1.2.2

Remove unnecessary parentheses.

$24 (4 x - 1) (x - 1) = 0$

Step 2

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

$4 x - 1 = 0$

$x - 1 = 0$

Step 3

Set $4 x - 1$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 3.1

Set $4 x - 1$ equal to $0$ .

$4 x - 1 = 0$

Step 3.2

Solve $4 x - 1 = 0$ for $x$ .

Tap for more steps...

Step 3.2.1

Add $1$ to both sides of the equation.

$4 x = 1$

Step 3.2.2

Divide each term in $4 x = 1$ by $4$ and simplify.

Tap for more steps...

Step 3.2.2.1

Divide each term in $4 x = 1$ by $4$ .

$\frac{4 x}{4} = \frac{1}{4}$

Step 3.2.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{4}$

Step 4

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

Tap for more steps...

Step 4.1

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

$x - 1 = 0$

Step 4.2

Add $1$ to both sides of the equation.

$x = 1$

Step 5

The final solution is all the values that make $24 (4 x - 1) (x - 1) = 0$ true.

$x = \frac{1}{4}, 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}, 1$

Decimal Form:

$x = 0.25, 1$