Solve for x -8x^4-10x^3+8x^2+10x=0

$- 8 x^{4} - 10 x^{3} + 8 x^{2} + 10 x = 0$

Step 1

Factor the left side of the equation.

Factor $2 x$ out of $- 8 x^{4} - 10 x^{3} + 8 x^{2} + 10 x$ .

Factor $2 x$ out of $- 8 x^{4}$ .

$2 x (- 4 x^{3}) - 10 x^{3} + 8 x^{2} + 10 x = 0$

Factor $2 x$ out of $- 10 x^{3}$ .

$2 x (- 4 x^{3}) + 2 x (- 5 x^{2}) + 8 x^{2} + 10 x = 0$

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

$2 x (- 4 x^{3}) + 2 x (- 5 x^{2}) + 2 x (4 x) + 10 x = 0$

Factor $2 x$ out of $10 x$ .

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

Factor $2 x$ out of $2 x (- 4 x^{3}) + 2 x (- 5 x^{2})$ .

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

Factor $2 x$ out of $2 x (- 4 x^{3} - 5 x^{2}) + 2 x (4 x)$ .

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

Factor $2 x$ out of $2 x (- 4 x^{3} - 5 x^{2} + 4 x) + 2 x (5)$ .

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

$2 x (x^{2} (- 4 x - 5) - (- 4 x - 5)) = 0$

Factor the polynomial by factoring out the greatest common factor, $- 4 x - 5$ .

$2 x ((- 4 x - 5) (x^{2} - 1)) = 0$

Rewrite $1$ as $1^{2}$ .

$2 x ((- 4 x - 5) (x^{2} - 1^{2})) = 0$

Factor.

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 $b = 1$ .

$2 x ((- 4 x - 5) ((x + 1) (x - 1))) = 0$

Remove unnecessary parentheses.

$2 x ((- 4 x - 5) (x + 1) (x - 1)) = 0$

Remove unnecessary parentheses.

$2 x (- 4 x - 5) (x + 1) (x - 1) = 0$

Step 2

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

$x = 0$

$- 4 x - 5 = 0$

$x + 1 = 0$

$x - 1 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $- 4 x - 5$ equal to $0$ and solve for $x$ .

Set $- 4 x - 5$ equal to $0$ .

$- 4 x - 5 = 0$

Solve $- 4 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$- 4 x = 5$

Divide each term in $- 4 x = 5$ by $- 4$ and simplify.

Divide each term in $- 4 x = 5$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{5}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{5}{- 4}$

Divide $x$ by $1$ .

$x = \frac{5}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{4}$

Step 5

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 6

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 7

The final solution is all the values that make $2 x (- 4 x - 5) (x + 1) (x - 1) = 0$ true.

$x = 0, - \frac{5}{4}, - 1, 1$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{5}{4}, - 1, 1$

Decimal Form:

$x = 0, - 1.25, - 1, 1$

Mixed Number Form:

$x = 0, - 1 \frac{1}{4}, - 1, 1$

Solve for x -8x^4-10x^3+8x^2+10x=0

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