Solve for a 6(a-5)=105

$6 (a - 5) = 105$

Step 1

Divide each term in $6 (a - 5) = 105$ by $6$ and simplify.

Divide each term in $6 (a - 5) = 105$ by $6$ .

$\frac{6 (a - 5)}{6} = \frac{105}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 (a - 5)}{6} = \frac{105}{6}$

Divide $a - 5$ by $1$ .

$a - 5 = \frac{105}{6}$

Simplify the right side.

Cancel the common factor of $105$ and $6$ .

Factor $3$ out of $105$ .

$a - 5 = \frac{3 (35)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$a - 5 = \frac{3 \cdot 35}{3 \cdot 2}$

Cancel the common factor.

$a - 5 = \frac{3 \cdot 35}{3 \cdot 2}$

Rewrite the expression.

$a - 5 = \frac{35}{2}$

Step 2

Move all terms not containing $a$ to the right side of the equation.

Add $5$ to both sides of the equation.

$a = \frac{35}{2} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a = \frac{35}{2} + 5 \cdot \frac{2}{2}$

Combine $5$ and $\frac{2}{2}$ .

$a = \frac{35}{2} + \frac{5 \cdot 2}{2}$

Combine the numerators over the common denominator.

$a = \frac{35 + 5 \cdot 2}{2}$

Simplify the numerator.

Multiply $5$ by $2$ .

$a = \frac{35 + 10}{2}$

Add $35$ and $10$ .

$a = \frac{45}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = \frac{45}{2}$

Decimal Form:

$a = 22.5$

Mixed Number Form:

$a = 22 \frac{1}{2}$