Solve for m 5(1+2m)=1/2(8+20m)

$5 (1 + 2 m) = \frac{1}{2} (8 + 20 m)$

Step 1

Simplify $5 (1 + 2 m)$ .

Start simplifying.

$0 + 0 + 5 (1 + 2 m) = \frac{1}{2} \cdot (8 + 20 m)$

Simplify by adding zeros.

$5 (1 + 2 m) = \frac{1}{2} \cdot (8 + 20 m)$

Apply the distributive property.

$5 \cdot 1 + 5 (2 m) = \frac{1}{2} \cdot (8 + 20 m)$

Multiply.

Multiply $5$ by $1$ .

$5 + 5 (2 m) = \frac{1}{2} \cdot (8 + 20 m)$

Multiply $2$ by $5$ .

$5 + 10 m = \frac{1}{2} \cdot (8 + 20 m)$

Step 2

Simplify $\frac{1}{2} \cdot (8 + 20 m)$ .

Apply the distributive property.

$5 + 10 m = \frac{1}{2} \cdot 8 + \frac{1}{2} (20 m)$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$5 + 10 m = \frac{1}{2} \cdot (2 (4)) + \frac{1}{2} (20 m)$

Cancel the common factor.

$5 + 10 m = \frac{1}{2} \cdot (2 \cdot 4) + \frac{1}{2} (20 m)$

Rewrite the expression.

$5 + 10 m = 4 + \frac{1}{2} (20 m)$

Cancel the common factor of $2$ .

Factor $2$ out of $20 m$ .

$5 + 10 m = 4 + \frac{1}{2} (2 (10 m))$

Cancel the common factor.

$5 + 10 m = 4 + \frac{1}{2} (2 (10 m))$

Rewrite the expression.

$5 + 10 m = 4 + 10 m$

Step 3

Move all terms containing $m$ to the left side of the equation.

Subtract $10 m$ from both sides of the equation.

$5 + 10 m - 10 m = 4$

Combine the opposite terms in $5 + 10 m - 10 m$ .

Subtract $10 m$ from $10 m$ .

$5 + 0 = 4$

Add $5$ and $0$ .

$5 = 4$

Step 4

Since $5 \neq 4$ , there are no solutions.

No solution