Algebra Examples

$(x + 4) (x - 3) = - 10$

Step 1

Simplify $(x + 4) (x - 3)$ .

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Step 1.1

Expand $(x + 4) (x - 3)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$x (x - 3) + 4 (x - 3) = - 10$

Step 1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 4 (x - 3) = - 10$

Step 1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 4 x + 4 \cdot - 3 = - 10$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 + 4 x + 4 \cdot - 3 = - 10$

Step 1.2.1.2

Move $- 3$ to the left of $x$ .

$x^{2} - 3 \cdot x + 4 x + 4 \cdot - 3 = - 10$

Step 1.2.1.3

Multiply $4$ by $- 3$ .

$x^{2} - 3 x + 4 x - 12 = - 10$

Step 1.2.2

Add $- 3 x$ and $4 x$ .

$x^{2} + x - 12 = - 10$

Step 2

Add $10$ to both sides of the equation.

$x^{2} + x - 12 + 10 = 0$

Step 3

Add $- 12$ and $10$ .

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

Step 4

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

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Step 4.1

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 $- 2$ and whose sum is $1$ .

$- 1, 2$

Step 4.2

Write the factored form using these integers.

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

Step 5

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

$x - 1 = 0$

$x + 2 = 0$

Step 6

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

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Step 6.1

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

$x - 1 = 0$

Step 6.2

Add $1$ to both sides of the equation.

$x = 1$

Step 7

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

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Step 7.1

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

$x + 2 = 0$

Step 7.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 8

The final solution is all the values that make $(x - 1) (x + 2) = 0$ true.

$x = 1, - 2$

Step 9