Solve the Inequality for a a(a-4)-a^2>12-6a

$a (a - 4) - a^{2} > 12 - 6 a$

Simplify $a (a - 4) - a^{2}$ .

Simplify each term.

Apply the distributive property.

$a \cdot a + a \cdot - 4 - a^{2} > 12 - 6 a$

Multiply $a$ by $a$ .

$a^{2} + a \cdot - 4 - a^{2} > 12 - 6 a$

Move $- 4$ to the left of $a$ .

$a^{2} - 4 a - a^{2} > 12 - 6 a$

Combine the opposite terms in $a^{2} - 4 a - a^{2}$ .

Subtract $a^{2}$ from $a^{2}$ .

$- 4 a + 0 > 12 - 6 a$

Add $- 4 a$ and $0$ .

$- 4 a > 12 - 6 a$

Move all terms containing $a$ to the left side of the inequality.

Add $6 a$ to both sides of the inequality.

$- 4 a + 6 a > 12$

Add $- 4 a$ and $6 a$ .

$2 a > 12$

Divide each term in $2 a > 12$ by $2$ and simplify.

Divide each term in $2 a > 12$ by $2$ .

$\frac{2 a}{2} > \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} > \frac{12}{2}$

Divide $a$ by $1$ .

$a > \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$a > 6$

The result can be shown in multiple forms.

Inequality Form:

$a > 6$

Interval Notation:

$(6, \infty)$