Solve by Factoring -4x^2-8x-3=-3-5x^2

$- 4 x^{2} - 8 x - 3 = - 3 - 5 x^{2}$

Step 1

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

Add $3$ to both sides of the equation.

$- 4 x^{2} - 8 x - 3 + 3 = - 5 x^{2}$

Add $5 x^{2}$ to both sides of the equation.

$- 4 x^{2} - 8 x - 3 + 3 + 5 x^{2} = 0$

Step 2

Simplify $- 4 x^{2} - 8 x - 3 + 3 + 5 x^{2}$ .

Combine the opposite terms in $- 4 x^{2} - 8 x - 3 + 3 + 5 x^{2}$ .

Add $- 3$ and $3$ .

$- 4 x^{2} - 8 x + 0 + 5 x^{2} = 0$

Add $- 4 x^{2} - 8 x$ and $0$ .

$- 4 x^{2} - 8 x + 5 x^{2} = 0$

Add $- 4 x^{2}$ and $5 x^{2}$ .

$x^{2} - 8 x = 0$

Step 3

Factor $x$ out of $x^{2} - 8 x$ .

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

$x \cdot x - 8 x = 0$

Factor $x$ out of $- 8 x$ .

$x \cdot x + x \cdot - 8 = 0$

Factor $x$ out of $x \cdot x + x \cdot - 8$ .

$x (x - 8) = 0$

Step 4

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

$x = 0$

$x - 8 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Step 7

The final solution is all the values that make $x (x - 8) = 0$ true.

$x = 0, 8$