How to solve h/2=3/N+5N-21

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve h/2=3/N+5N-21 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$h/2=3/N+5N-21$$

Solve for h

$h=10N-42+\frac{6}{N}$
$N\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $2N$, the least common multiple of $2,N$.

$$Nh=2\times 3+5N\times 2N+2N\left(-21\right)$$

Multiply $N$ and $N$ to get $N^{2}$.

$$Nh=2\times 3+5N^{2}\times 2+2N\left(-21\right)$$

Multiply $2$ and $3$ to get $6$.

$$Nh=6+5N^{2}\times 2+2N\left(-21\right)$$

Multiply $5$ and $2$ to get $10$.

$$Nh=6+10N^{2}+2N\left(-21\right)$$

Multiply $2$ and $-21$ to get $-42$.

$$Nh=6+10N^{2}-42N$$

The equation is in standard form.

$$Nh=10N^{2}-42N+6$$

Divide both sides by $N$.

$$\frac{Nh}{N}=\frac{10N^{2}-42N+6}{N}$$

Dividing by $N$ undoes the multiplication by $N$.

$$h=\frac{10N^{2}-42N+6}{N}$$

Divide $6+10N^{2}-42N$ by $N$.

$$h=10N-42+\frac{6}{N}$$

Show Solution

Solve for N (complex solution)

$N=\frac{\sqrt{h^{2}+84h+1524}+h+42}{20}$
$N=\frac{-\sqrt{h^{2}+84h+1524}+h+42}{20}$

Solve for N

$N=\frac{\sqrt{h^{2}+84h+1524}+h+42}{20}$
$N=\frac{-\sqrt{h^{2}+84h+1524}+h+42}{20}\text{, }h\geq 4\sqrt{15}-42\text{ or }h\leq -4\sqrt{15}-42$