Solve 6=a(a+4)(0-2)

$$6 = a ( a + 4 ) ( 0 - 2 )$$

Solve for a

$$a=-3$$

$$a=-1$$

Steps Using the Quadratic Formula

Subtract 2 from 0 to get -2.

$$6=a\left(a+4\right)\left(-2\right)$$

Use the distributive property to multiply a by a+4.

$$6=\left(a^{2}+4a\right)\left(-2\right)$$

Use the distributive property to multiply a^{2}+4a by -2.

$$6=-2a^{2}-8a$$

Swap sides so that all variable terms are on the left hand side.

$$-2a^{2}-8a=6$$

Subtract 6 from both sides.

$$-2a^{2}-8a-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, -8 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-2\right)\left(-6\right)}}{2\left(-2\right)}$$

Square -8.

$$a=\frac{-\left(-8\right)±\sqrt{64-4\left(-2\right)\left(-6\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$a=\frac{-\left(-8\right)±\sqrt{64+8\left(-6\right)}}{2\left(-2\right)}$$

Multiply 8 times -6.

$$a=\frac{-\left(-8\right)±\sqrt{64-48}}{2\left(-2\right)}$$

Add 64 to -48.

$$a=\frac{-\left(-8\right)±\sqrt{16}}{2\left(-2\right)}$$

Take the square root of 16.

$$a=\frac{-\left(-8\right)±4}{2\left(-2\right)}$$

The opposite of -8 is 8.

$$a=\frac{8±4}{2\left(-2\right)}$$

Multiply 2 times -2.

$$a=\frac{8±4}{-4}$$

Now solve the equation a=\frac{8±4}{-4} when ± is plus. Add 8 to 4.

$$a=\frac{12}{-4}$$

Divide 12 by -4.

$$a=-3$$

Now solve the equation a=\frac{8±4}{-4} when ± is minus. Subtract 4 from 8.

$$a=\frac{4}{-4}$$

Divide 4 by -4.

$$a=-1$$

The equation is now solved.

$$a=-3 a=-1$$

Steps for Completing the Square

Subtract 2 from 0 to get -2.

$$6=a\left(a+4\right)\left(-2\right)$$

Use the distributive property to multiply a by a+4.

$$6=\left(a^{2}+4a\right)\left(-2\right)$$

Use the distributive property to multiply a^{2}+4a by -2.

$$6=-2a^{2}-8a$$

Swap sides so that all variable terms are on the left hand side.

$$-2a^{2}-8a=6$$

Divide both sides by -2.

$$\frac{-2a^{2}-8a}{-2}=\frac{6}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$a^{2}+\left(-\frac{8}{-2}\right)a=\frac{6}{-2}$$

Divide -8 by -2.

$$a^{2}+4a=\frac{6}{-2}$$

Divide 6 by -2.

$$a^{2}+4a=-3$$

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$a^{2}+4a+2^{2}=-3+2^{2}$$

Square 2.

$$a^{2}+4a+4=-3+4$$

Add -3 to 4.

$$a^{2}+4a+4=1$$

Factor a^{2}+4a+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(a+2\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(a+2\right)^{2}}=\sqrt{1}$$

Simplify.

$$a+2=1 a+2=-1$$

Subtract 2 from both sides of the equation.

$$a=-1 a=-3$$