Solve for d -d^2-12d+4=-6d^2

$- d^{2} - 12 d + 4 = - 6 d^{2}$

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

Add $6 d^{2}$ to both sides of the equation.

$- d^{2} - 12 d + 4 + 6 d^{2} = 0$

Add $- d^{2}$ and $6 d^{2}$ .

$5 d^{2} - 12 d + 4 = 0$

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 $a \cdot c = 5 \cdot 4 = 20$ and whose sum is $b = - 12$ .

Factor $- 12$ out of $- 12 d$ .

$5 d^{2} - 12 d + 4 = 0$

Rewrite $- 12$ as $- 2$ plus $- 10$

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

Apply the distributive property.

$5 d^{2} - 2 d - 10 d + 4 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$d (5 d - 2) - 2 (5 d - 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 d - 2$ .

$(5 d - 2) (d - 2) = 0$

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

$5 d - 2 = 0$

$d - 2 = 0$

Set $5 d - 2$ equal to $0$ and solve for $d$ .

Set $5 d - 2$ equal to $0$ .

$5 d - 2 = 0$

Solve $5 d - 2 = 0$ for $d$ .

Add $2$ to both sides of the equation.

$5 d = 2$

Divide each term in $5 d = 2$ by $5$ and simplify.

Divide each term in $5 d = 2$ by $5$ .

$\frac{5 d}{5} = \frac{2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 d}{5} = \frac{2}{5}$

Divide $d$ by $1$ .

$d = \frac{2}{5}$

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

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

$d - 2 = 0$

Add $2$ to both sides of the equation.

$d = 2$

The final solution is all the values that make $(5 d - 2) (d - 2) = 0$ true.

$d = \frac{2}{5}, 2$

The result can be shown in multiple forms.

Exact Form:

$d = \frac{2}{5}, 2$

Decimal Form:

$d = 0.4, 2$

Solve for d -d^2-12d+4=-6d^2

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