Solve for x 3x^2-7x-9=4x^2-4x-9

$3 x^{2} - 7 x - 9 = 4 x^{2} - 4 x - 9$

Step 1

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

Subtract $4 x^{2}$ from both sides of the equation.

$3 x^{2} - 7 x - 9 - 4 x^{2} = - 4 x - 9$

Add $4 x$ to both sides of the equation.

$3 x^{2} - 7 x - 9 - 4 x^{2} + 4 x = - 9$

Subtract $4 x^{2}$ from $3 x^{2}$ .

$- x^{2} - 7 x - 9 + 4 x = - 9$

Add $- 7 x$ and $4 x$ .

$- x^{2} - 3 x - 9 = - 9$

Step 2

Add $9$ to both sides of the equation.

$- x^{2} - 3 x - 9 + 9 = 0$

Step 3

Combine the opposite terms in $- x^{2} - 3 x - 9 + 9$ .

Add $- 9$ and $9$ .

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

Add $- x^{2} - 3 x$ and $0$ .

$- x^{2} - 3 x = 0$

Step 4

Factor $- x$ out of $- x^{2} - 3 x$ .

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

$- x \cdot x - 3 x = 0$

Factor $- x$ out of $- 3 x$ .

$- x \cdot x - x \cdot 3 = 0$

Factor $- x$ out of $- x (x) - x (3)$ .

$- x (x + 3) = 0$

Step 5

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

$x = 0$

$x + 3 = 0$

Step 6

Set $x$ equal to $0$ .

$x = 0$

Step 7

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 8

The final solution is all the values that make $- x (x + 3) = 0$ true.

$x = 0, - 3$