Finite Math Examples

$3 x (x + 1) + x (5 - 2 x) = 0$

Step 1

Simplify $3 x (x + 1) + x (5 - 2 x)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 1 + x (5 - 2 x) = 0$

Step 1.1.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.1.2.1

Move $x$ .

$3 (x \cdot x) + 3 x \cdot 1 + x (5 - 2 x) = 0$

Step 1.1.2.2

Multiply $x$ by $x$ .

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

Step 1.1.3

Multiply $3$ by $1$ .

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

Step 1.1.4

Apply the distributive property.

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

Step 1.1.5

Move $5$ to the left of $x$ .

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

Step 1.1.6

Rewrite using the commutative property of multiplication.

$3 x^{2} + 3 x + 5 \cdot x - 2 x \cdot x = 0$

Step 1.1.7

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.1.7.1

Move $x$ .

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

Step 1.1.7.2

Multiply $x$ by $x$ .

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

Step 1.2

Simplify by adding terms.

Tap for more steps...

Step 1.2.1

Subtract $2 x^{2}$ from $3 x^{2}$ .

$x^{2} + 3 x + 5 x = 0$

Step 1.2.2

Add $3 x$ and $5 x$ .

$x^{2} + 8 x = 0$

Step 2

Factor $x$ out of $x^{2} + 8 x$ .

Tap for more steps...

Step 2.1

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

$x \cdot x + 8 x = 0$

Step 2.2

Factor $x$ out of $8 x$ .

$x \cdot x + x \cdot 8 = 0$

Step 2.3

Factor $x$ out of $x \cdot x + x \cdot 8$ .

$x (x + 8) = 0$

Step 3

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

$x = 0$

$x + 8 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x + 8$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 5.1

Set $x + 8$ equal to $0$ .

$x + 8 = 0$

Step 5.2

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 6

The final solution is all the values that make $x (x + 8) = 0$ true.

$x = 0, - 8$