Solve by Factoring x^2+5x-33=4x+9

$x^{2} + 5 x - 33 = 4 x + 9$

Step 1

Move all the expressions to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$x^{2} + 5 x - 33 - 4 x = 9$

Subtract $9$ from both sides of the equation.

$x^{2} + 5 x - 33 - 4 x - 9 = 0$

Step 2

Simplify $x^{2} + 5 x - 33 - 4 x - 9$ .

Subtract $4 x$ from $5 x$ .

$x^{2} + x - 33 - 9 = 0$

Subtract $9$ from $- 33$ .

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

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^2+5x-33=4x+9

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