Solve for d 5d^2+10d+8=2d^2

$5 d^{2} + 10 d + 8 = 2 d^{2}$

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

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

$5 d^{2} + 10 d + 8 - 2 d^{2} = 0$

Subtract $2 d^{2}$ from $5 d^{2}$ .

$3 d^{2} + 10 d + 8 = 0$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot 8 = 24$ and whose sum is $b = 10$ .

Factor $10$ out of $10 d$ .

$3 d^{2} + 10 (d) + 8 = 0$

Rewrite $10$ as $4$ plus $6$

$3 d^{2} + (4 + 6) d + 8 = 0$

Apply the distributive property.

$3 d^{2} + 4 d + 6 d + 8 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 d^{2} + 4 d) + 6 d + 8 = 0$

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

$d (3 d + 4) + 2 (3 d + 4) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 d + 4$ .

$(3 d + 4) (d + 2) = 0$

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

$3 d + 4 = 0$

$d + 2 = 0$

Set $3 d + 4$ equal to $0$ and solve for $d$ .

Set $3 d + 4$ equal to $0$ .

$3 d + 4 = 0$

Solve $3 d + 4 = 0$ for $d$ .

Subtract $4$ from both sides of the equation.

$3 d = - 4$

Divide each term in $3 d = - 4$ by $3$ and simplify.

Divide each term in $3 d = - 4$ by $3$ .

$\frac{3 d}{3} = \frac{- 4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 d}{3} = \frac{- 4}{3}$

Divide $d$ by $1$ .

$d = \frac{- 4}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$d = - \frac{4}{3}$

Set $d + 2$ equal to $0$ and solve for $d$ .

Set $d + 2$ equal to $0$ .

$d + 2 = 0$

Subtract $2$ from both sides of the equation.

$d = - 2$

The final solution is all the values that make $(3 d + 4) (d + 2) = 0$ true.

$d = - \frac{4}{3}, - 2$

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{4}{3}, - 2$

Decimal Form:

$d = - 1.\overline{3}, - 2$

Mixed Number Form:

$d = - 1 \frac{1}{3}, - 2$

Solve for d 5d^2+10d+8=2d^2

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