Solve by Factoring x^2+3x-24=3x+1

$x^{2} + 3 x - 24 = 3 x + 1$

Step 1

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

Subtract $3 x$ from both sides of the equation.

$x^{2} + 3 x - 24 - 3 x = 1$

Subtract $1$ from both sides of the equation.

$x^{2} + 3 x - 24 - 3 x - 1 = 0$

Step 2

Simplify $x^{2} + 3 x - 24 - 3 x - 1$ .

Combine the opposite terms in $x^{2} + 3 x - 24 - 3 x - 1$ .

Subtract $3 x$ from $3 x$ .

$x^{2} + 0 - 24 - 1 = 0$

Add $x^{2}$ and $0$ .

$x^{2} - 24 - 1 = 0$

Subtract $1$ from $- 24$ .

$x^{2} - 25 = 0$

Step 3

Rewrite $25$ as $5^{2}$ .

$x^{2} - 5^{2} = 0$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$(x + 5) (x - 5) = 0$

Step 5

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

$x + 5 = 0$

$x - 5 = 0$

Step 6

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 7

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Step 8

The final solution is all the values that make $(x + 5) (x - 5) = 0$ true.

$x = - 5, 5$