Algebra Examples

$(x + 4) (x + 1) = 2 (x - 2) (x + 1)$

Step 1

Simplify $(x + 4) (x + 1)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + (x + 4) (x + 1) = 2 (x - 2) (x + 1)$

Step 1.2

Simplify by adding zeros.

$(x + 4) (x + 1) = 2 (x - 2) (x + 1)$

Step 1.3

Expand $(x + 4) (x + 1)$ using the FOIL Method.

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$x (x + 1) + 4 (x + 1) = 2 (x - 2) (x + 1)$

Step 1.3.2

Apply the distributive property.

$x \cdot x + x \cdot 1 + 4 (x + 1) = 2 (x - 2) (x + 1)$

Step 1.3.3

Apply the distributive property.

$x \cdot x + x \cdot 1 + 4 x + 4 \cdot 1 = 2 (x - 2) (x + 1)$

Step 1.4

Simplify and combine like terms.

Tap for more steps...

Step 1.4.1

Simplify each term.

Tap for more steps...

Step 1.4.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 + 4 x + 4 \cdot 1 = 2 (x - 2) (x + 1)$

Step 1.4.1.2

Multiply $x$ by $1$ .

$x^{2} + x + 4 x + 4 \cdot 1 = 2 (x - 2) (x + 1)$

Step 1.4.1.3

Multiply $4$ by $1$ .

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

Step 1.4.2

Add $x$ and $4 x$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Simplify by multiplying through.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$x^{2} + 5 x + 4 = (2 x + 2 \cdot - 2) (x + 1)$

Step 2.1.2

Multiply $2$ by $- 2$ .

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

Step 2.2

Expand $(2 x - 4) (x + 1)$ using the FOIL Method.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

Apply the distributive property.

$x^{2} + 5 x + 4 = 2 x \cdot x + 2 x \cdot 1 - 4 (x + 1)$

Step 2.2.3

Apply the distributive property.

$x^{2} + 5 x + 4 = 2 x \cdot x + 2 x \cdot 1 - 4 x - 4 \cdot 1$

Step 2.3

Simplify and combine like terms.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

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

Tap for more steps...

Step 2.3.1.1.1

Move $x$ .

$x^{2} + 5 x + 4 = 2 (x \cdot x) + 2 x \cdot 1 - 4 x - 4 \cdot 1$

Step 2.3.1.1.2

Multiply $x$ by $x$ .

$x^{2} + 5 x + 4 = 2 x^{2} + 2 x \cdot 1 - 4 x - 4 \cdot 1$

Step 2.3.1.2

Multiply $2$ by $1$ .

$x^{2} + 5 x + 4 = 2 x^{2} + 2 x - 4 x - 4 \cdot 1$

Step 2.3.1.3

Multiply $- 4$ by $1$ .

$x^{2} + 5 x + 4 = 2 x^{2} + 2 x - 4 x - 4$

Step 2.3.2

Subtract $4 x$ from $2 x$ .

$x^{2} + 5 x + 4 = 2 x^{2} - 2 x - 4$

Step 3

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

Tap for more steps...

Step 3.1

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

$x^{2} + 5 x + 4 - 2 x^{2} = - 2 x - 4$

Step 3.2

Add $2 x$ to both sides of the equation.

$x^{2} + 5 x + 4 - 2 x^{2} + 2 x = - 4$

Step 3.3

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

$- x^{2} + 5 x + 4 + 2 x = - 4$

Step 3.4

Add $5 x$ and $2 x$ .

$- x^{2} + 7 x + 4 = - 4$

Step 4

Add $4$ to both sides of the equation.

$- x^{2} + 7 x + 4 + 4 = 0$

Step 5

Add $4$ and $4$ .

$- x^{2} + 7 x + 8 = 0$

Step 6

Factor the left side of the equation.

Tap for more steps...

Step 6.1

Factor $- 1$ out of $- x^{2} + 7 x + 8$ .

Tap for more steps...

Step 6.1.1

Factor $- 1$ out of $- x^{2}$ .

$- (x^{2}) + 7 x + 8 = 0$

Step 6.1.2

Factor $- 1$ out of $7 x$ .

$- (x^{2}) - (- 7 x) + 8 = 0$

Step 6.1.3

Rewrite $8$ as $- 1 (- 8)$ .

$- (x^{2}) - (- 7 x) - 1 \cdot - 8 = 0$

Step 6.1.4

Factor $- 1$ out of $- (x^{2}) - (- 7 x)$ .

$- (x^{2} - 7 x) - 1 \cdot - 8 = 0$

Step 6.1.5

Factor $- 1$ out of $- (x^{2} - 7 x) - 1 (- 8)$ .

$- (x^{2} - 7 x - 8) = 0$

Step 6.2

Factor.

Tap for more steps...

Step 6.2.1

Factor $x^{2} - 7 x - 8$ using the AC method.

Tap for more steps...

Step 6.2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 8$ and whose sum is $- 7$ .

$- 8, 1$

Step 6.2.1.2

Write the factored form using these integers.

$- ((x - 8) (x + 1)) = 0$

Step 6.2.2

Remove unnecessary parentheses.

$- (x - 8) (x + 1) = 0$

Step 7

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

$x - 8 = 0$

$x + 1 = 0$

Step 8

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

Tap for more steps...

Step 8.1

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

$x - 8 = 0$

Step 8.2

Add $8$ to both sides of the equation.

$x = 8$

Step 9

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

Tap for more steps...

Step 9.1

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

$x + 1 = 0$

Step 9.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 10

The final solution is all the values that make $- (x - 8) (x + 1) = 0$ true.

$x = 8, - 1$