Solve 12n^2/4^2+ny-20

$$12 \frac { n ^ { 2 } } { 4 ^ { 2 } } + n y - 20$$

Evaluate

$$ny+\frac{3n^{2}}{4}-20$$

Short Solution Steps

Calculate 4 to the power of 2 and get 16.

$$12\times \frac{n^{2}}{16}+ny-20$$

Express 12\times \frac{n^{2}}{16} as a single fraction.

$$\frac{12n^{2}}{16}+ny-20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply ny-20 times \frac{16}{16}.

$$\frac{12n^{2}}{16}+\frac{16\left(ny-20\right)}{16}$$

Since \frac{12n^{2}}{16} and \frac{16\left(ny-20\right)}{16} have the same denominator, add them by adding their numerators.

$$\frac{12n^{2}+16\left(ny-20\right)}{16}$$

Do the multiplications in 12n^{2}+16\left(ny-20\right).

$$\frac{12n^{2}+16ny-320}{16}$$

Factor

$$\frac{4ny+3n^{2}-80}{4}$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$factor(12\times \frac{n^{2}}{16}+ny-20)$$

Express 12\times \frac{n^{2}}{16} as a single fraction.

$$factor(\frac{12n^{2}}{16}+ny-20)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply ny-20 times \frac{16}{16}.

$$factor(\frac{12n^{2}}{16}+\frac{16\left(ny-20\right)}{16})$$

Since \frac{12n^{2}}{16} and \frac{16\left(ny-20\right)}{16} have the same denominator, add them by adding their numerators.

$$factor(\frac{12n^{2}+16\left(ny-20\right)}{16})$$

Do the multiplications in 12n^{2}+16\left(ny-20\right).

$$factor(\frac{12n^{2}+16ny-320}{16})$$

Consider 12n^{2}+16ny-320. Factor out 4.

$$4\left(3n^{2}+4ny-80\right)$$

Rewrite the complete factored expression. Simplify.

$$\frac{3n^{2}+4ny-80}{4}$$