Solve 2a=-6a/a-4

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

Solve for a

$$a=1$$

$$a=0$$

Steps Using Factoring

Variable a cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by a-4.

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

Use the distributive property to multiply 2a by a-4.

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

Add 6a to both sides.

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

Combine -8a and 6a to get -2a.

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

Factor out a.

$$a\left(2a-2\right)=0$$

To find equation solutions, solve a=0 and 2a-2=0.

$$a=0 a=1$$

Steps Using the Quadratic Formula

Variable a cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by a-4.

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

Use the distributive property to multiply 2a by a-4.

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

Add 6a to both sides.

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

Combine -8a and 6a to get -2a.

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

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

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

Take the square root of \left(-2\right)^{2}.

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

The opposite of -2 is 2.

$$a=\frac{2±2}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{2±2}{4}$$

Now solve the equation a=\frac{2±2}{4} when ± is plus. Add 2 to 2.

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

Divide 4 by 4.

$$a=1$$

Now solve the equation a=\frac{2±2}{4} when ± is minus. Subtract 2 from 2.

$$a=\frac{0}{4}$$

Divide 0 by 4.

$$a=0$$

The equation is now solved.

$$a=1 a=0$$

Steps for Completing the Square

Variable a cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by a-4.

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

Use the distributive property to multiply 2a by a-4.

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

Add 6a to both sides.

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

Combine -8a and 6a to get -2a.

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

Divide both sides by 2.

$$\frac{2a^{2}-2a}{2}=\frac{0}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a^{2}+\left(-\frac{2}{2}\right)a=\frac{0}{2}$$

Divide -2 by 2.

$$a^{2}-a=\frac{0}{2}$$

Divide 0 by 2.

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

Divide -1, the coefficient of the x term, by 2 to get -\frac{1}{2}. Then add the square of -\frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$a^{2}-a+\frac{1}{4}=\frac{1}{4}$$

Factor a^{2}-a+\frac{1}{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}.

$$\left(a-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(a-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Simplify.

$$a-\frac{1}{2}=\frac{1}{2} a-\frac{1}{2}=-\frac{1}{2}$$

Add \frac{1}{2} to both sides of the equation.

$$a=1 a=0$$