Algebra Examples

$5 (x + 3) - 5 (x^{2} - 1) = x^{2} + 7 (3 - x) - 1$

Step 1

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

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$5 x + 5 \cdot 3 - 5 (x^{2} - 1) = x^{2} + 7 (3 - x) - 1$

Step 1.1.2

Multiply $5$ by $3$ .

$5 x + 15 - 5 (x^{2} - 1) = x^{2} + 7 (3 - x) - 1$

Step 1.1.3

Apply the distributive property.

$5 x + 15 - 5 x^{2} - 5 \cdot - 1 = x^{2} + 7 (3 - x) - 1$

Step 1.1.4

Multiply $- 5$ by $- 1$ .

$5 x + 15 - 5 x^{2} + 5 = x^{2} + 7 (3 - x) - 1$

Step 1.2

Add $15$ and $5$ .

$5 x - 5 x^{2} + 20 = x^{2} + 7 (3 - x) - 1$

Step 2

Simplify $x^{2} + 7 (3 - x) - 1$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$5 x - 5 x^{2} + 20 = x^{2} + 7 \cdot 3 + 7 (- x) - 1$

Step 2.1.2

Multiply $7$ by $3$ .

$5 x - 5 x^{2} + 20 = x^{2} + 21 + 7 (- x) - 1$

Step 2.1.3

Multiply $- 1$ by $7$ .

$5 x - 5 x^{2} + 20 = x^{2} + 21 - 7 x - 1$

Step 2.2

Subtract $1$ from $21$ .

$5 x - 5 x^{2} + 20 = x^{2} - 7 x + 20$

Step 3

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1

Subtract $x^{2}$ from both sides of the equation.

$5 x - 5 x^{2} + 20 - x^{2} = - 7 x + 20$

Step 3.2

Add $7 x$ to both sides of the equation.

$5 x - 5 x^{2} + 20 - x^{2} + 7 x = 20$

Step 3.3

Add $5 x$ and $7 x$ .

$- 5 x^{2} + 20 - x^{2} + 12 x = 20$

Step 3.4

Subtract $x^{2}$ from $- 5 x^{2}$ .

$- 6 x^{2} + 20 + 12 x = 20$

Step 4

Subtract $20$ from both sides of the equation.

$- 6 x^{2} + 20 + 12 x - 20 = 0$

Step 5

Combine the opposite terms in $- 6 x^{2} + 20 + 12 x - 20$ .

Tap for more steps...

Step 5.1

Subtract $20$ from $20$ .

$- 6 x^{2} + 12 x + 0 = 0$

Step 5.2

Add $- 6 x^{2} + 12 x$ and $0$ .

$- 6 x^{2} + 12 x = 0$

Step 6

Factor $- 6 x$ out of $- 6 x^{2} + 12 x$ .

Tap for more steps...

Step 6.1

Factor $- 6 x$ out of $- 6 x^{2}$ .

$- 6 x \cdot x + 12 x = 0$

Step 6.2

Factor $- 6 x$ out of $12 x$ .

$- 6 x \cdot x - 6 x \cdot - 2 = 0$

Step 6.3

Factor $- 6 x$ out of $- 6 x (x) - 6 x (- 2)$ .

$- 6 x (x - 2) = 0$

Step 7

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

$x = 0$

$x - 2 = 0$

Step 8

Set $x$ equal to $0$ .

$x = 0$

Step 9

Set $x - 2$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 9.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 9.2

Add $2$ to both sides of the equation.

$x = 2$

Step 10

The final solution is all the values that make $- 6 x (x - 2) = 0$ true.

$x = 0, 2$