Solve 2c+12/2-c*(6-c)=0

$$\frac { 2 c + 12 } { 2 - c } \cdot ( 6 - c ) = 0$$

Solve for c

$$c=6$$

$$c=-6$$

Steps by Finding Square Root

Variable c cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -c+2.

$$\left(2c+12\right)\left(6-c\right)=0$$

Use the distributive property to multiply 2c+12 by 6-c and combine like terms.

$$-2c^{2}+72=0$$

Subtract 72 from both sides. Anything subtracted from zero gives its negation.

$$-2c^{2}=-72$$

Divide both sides by -2.

$$c^{2}=\frac{-72}{-2}$$

Divide -72 by -2 to get 36.

$$c^{2}=36$$

Take the square root of both sides of the equation.

$$c=6 c=-6$$

Steps Using the Quadratic Formula

Variable c cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -c+2.

$$\left(2c+12\right)\left(6-c\right)=0$$

Use the distributive property to multiply 2c+12 by 6-c and combine like terms.

$$-2c^{2}+72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 72}}{2\left(-2\right)}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-2\right)\times 72}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$c=\frac{0±\sqrt{8\times 72}}{2\left(-2\right)}$$

Multiply 8 times 72.

$$c=\frac{0±\sqrt{576}}{2\left(-2\right)}$$

Take the square root of 576.

$$c=\frac{0±24}{2\left(-2\right)}$$

Multiply 2 times -2.

$$c=\frac{0±24}{-4}$$

Now solve the equation c=\frac{0±24}{-4} when ± is plus. Divide 24 by -4.

$$c=-6$$

Now solve the equation c=\frac{0±24}{-4} when ± is minus. Divide -24 by -4.

$$c=6$$

The equation is now solved.

$$c=-6 c=6$$