Solve by Factoring (x-3)(x+4)=30

$(x - 3) (x + 4) = 30$

Step 1

Subtract $30$ from both sides of the equation.

$(x - 3) (x + 4) - 30 = 0$

Step 2

Simplify $(x - 3) (x + 4) - 30$ .

Simplify each term.

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

Apply the distributive property.

$x (x + 4) - 3 (x + 4) - 30 = 0$

Apply the distributive property.

$x \cdot x + x \cdot 4 - 3 (x + 4) - 30 = 0$

Apply the distributive property.

$x \cdot x + x \cdot 4 - 3 x - 3 \cdot 4 - 30 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 4 - 3 x - 3 \cdot 4 - 30 = 0$

Move $4$ to the left of $x$ .

$x^{2} + 4 \cdot x - 3 x - 3 \cdot 4 - 30 = 0$

Multiply $- 3$ by $4$ .

$x^{2} + 4 x - 3 x - 12 - 30 = 0$

Subtract $3 x$ from $4 x$ .

$x^{2} + x - 12 - 30 = 0$

Subtract $30$ from $- 12$ .

$x^{2} + x - 42 = 0$

Step 3

Factor $x^{2} + x - 42$ using the AC method.

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 $- 42$ and whose sum is $1$ .

$- 6, 7$

Write the factored form using these integers.

$(x - 6) (x + 7) = 0$

Step 4

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

$x - 6 = 0$

$x + 7 = 0$

Step 5

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Step 6

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 7

The final solution is all the values that make $(x - 6) (x + 7) = 0$ true.

$x = 6, - 7$

Solve by Factoring (x-3)(x+4)=30

Related Questions

Support LCMGCF.com by disabling your adblocker.