Solve 450mm^2=(1/2)18mm(a+24mm)

$$450 mm ^ { 2 } = ( \frac { 1 } { 2 } ) 18 mm ( a + 24 mm )$$

Solve for a

$$\left\{\begin{matrix}\\a=-2m\left(12m-25\right)\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$450m^{3}=\frac{1}{2}\times 18mm\left(a+24mm\right)$$

Multiply m and m to get m^{2}.

$$450m^{3}=\frac{1}{2}\times 18mm\left(a+24m^{2}\right)$$

Multiply m and m to get m^{2}.

$$450m^{3}=\frac{1}{2}\times 18m^{2}\left(a+24m^{2}\right)$$

Multiply \frac{1}{2} and 18 to get 9.

$$450m^{3}=9m^{2}\left(a+24m^{2}\right)$$

Use the distributive property to multiply 9m^{2} by a+24m^{2}.

$$450m^{3}=9m^{2}a+216m^{4}$$

Swap sides so that all variable terms are on the left hand side.

$$9m^{2}a+216m^{4}=450m^{3}$$

Subtract 216m^{4} from both sides.

$$9m^{2}a=450m^{3}-216m^{4}$$

Divide both sides by 9m^{2}.

$$\frac{9m^{2}a}{9m^{2}}=\frac{18\left(25-12m\right)m^{3}}{9m^{2}}$$

Dividing by 9m^{2} undoes the multiplication by 9m^{2}.

$$a=\frac{18\left(25-12m\right)m^{3}}{9m^{2}}$$

Divide 18\left(25-12m\right)m^{3} by 9m^{2}.

$$a=2m\left(25-12m\right)$$

Solve for m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m=\frac{-\sqrt{625-24a}+25}{24}\text{; }m=\frac{\sqrt{625-24a}+25}{24}\text{, }&a\leq \frac{625}{24}\end{matrix}\right.$$