Solve 8+5(4z-1)=3(7z+2)THEN2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$8+5(4z-1)=3(7z+2)THEN2$$

Solve for E

$\left\{\begin{matrix}E=\frac{20z+3}{3HN_{2}T\left(7z+2\right)}\text{, }&N_{2}\neq 0\text{ and }H\neq 0\text{ and }T\neq 0\text{ and }z\neq -\frac{2}{7}\\E\in \mathrm{R}\text{, }&\left(T=0\text{ or }H=0\text{ or }N_{2}=0\right)\text{ and }z=-\frac{3}{20}\end{matrix}\right.$

Steps for Solving Linear Equation

Use the distributive property to multiply $5$ by $4z-1$.

$$8+20z-5=3\left(7z+2\right)THEN_{2}$$

Subtract $5$ from $8$ to get $3$.

$$3+20z=3\left(7z+2\right)THEN_{2}$$

Use the distributive property to multiply $3$ by $7z+2$.

$$3+20z=\left(21z+6\right)THEN_{2}$$

Use the distributive property to multiply $21z+6$ by $T$.

$$3+20z=\left(21zT+6T\right)HEN_{2}$$

Use the distributive property to multiply $21zT+6T$ by $H$.

$$3+20z=\left(21zTH+6TH\right)EN_{2}$$

Use the distributive property to multiply $21zTH+6TH$ by $E$.

$$3+20z=\left(21zTHE+6THE\right)N_{2}$$

Use the distributive property to multiply $21zTHE+6THE$ by $N_{2}$.

$$3+20z=21zTHEN_{2}+6THEN_{2}$$

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

$$21zTHEN_{2}+6THEN_{2}=3+20z$$

Combine all terms containing $E$.

$$\left(21zTHN_{2}+6THN_{2}\right)E=3+20z$$

The equation is in standard form.

$$\left(21HN_{2}Tz+6HN_{2}T\right)E=20z+3$$

Divide both sides by $6N_{2}HT+21zTHN_{2}$.

$$\frac{\left(21HN_{2}Tz+6HN_{2}T\right)E}{21HN_{2}Tz+6HN_{2}T}=\frac{20z+3}{21HN_{2}Tz+6HN_{2}T}$$

Dividing by $6N_{2}HT+21zTHN_{2}$ undoes the multiplication by $6N_{2}HT+21zTHN_{2}$.

$$E=\frac{20z+3}{21HN_{2}Tz+6HN_{2}T}$$

Divide $20z+3$ by $6N_{2}HT+21zTHN_{2}$.

$$E=\frac{20z+3}{3HN_{2}T\left(7z+2\right)}$$

Solve for H

$\left\{\begin{matrix}H=\frac{20z+3}{3EN_{2}T\left(7z+2\right)}\text{, }&N_{2}\neq 0\text{ and }E\neq 0\text{ and }T\neq 0\text{ and }z\neq -\frac{2}{7}\\H\in \mathrm{R}\text{, }&\left(T=0\text{ or }E=0\text{ or }N_{2}=0\right)\text{ and }z=-\frac{3}{20}\end{matrix}\right.$

Steps for Solving Linear Equation

Use the distributive property to multiply $5$ by $4z-1$.

$$8+20z-5=3\left(7z+2\right)THEN_{2}$$

Subtract $5$ from $8$ to get $3$.

$$3+20z=3\left(7z+2\right)THEN_{2}$$

Use the distributive property to multiply $3$ by $7z+2$.

$$3+20z=\left(21z+6\right)THEN_{2}$$

Use the distributive property to multiply $21z+6$ by $T$.

$$3+20z=\left(21zT+6T\right)HEN_{2}$$

Use the distributive property to multiply $21zT+6T$ by $H$.

$$3+20z=\left(21zTH+6TH\right)EN_{2}$$

Use the distributive property to multiply $21zTH+6TH$ by $E$.

$$3+20z=\left(21zTHE+6THE\right)N_{2}$$

Use the distributive property to multiply $21zTHE+6THE$ by $N_{2}$.

$$3+20z=21zTHEN_{2}+6THEN_{2}$$

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

$$21zTHEN_{2}+6THEN_{2}=3+20z$$

Combine all terms containing $H$.

$$\left(21zTEN_{2}+6TEN_{2}\right)H=3+20z$$

The equation is in standard form.

$$\left(21EN_{2}Tz+6EN_{2}T\right)H=20z+3$$

Divide both sides by $6N_{2}ET+21zTEN_{2}$.

$$\frac{\left(21EN_{2}Tz+6EN_{2}T\right)H}{21EN_{2}Tz+6EN_{2}T}=\frac{20z+3}{21EN_{2}Tz+6EN_{2}T}$$

Dividing by $6N_{2}ET+21zTEN_{2}$ undoes the multiplication by $6N_{2}ET+21zTEN_{2}$.

$$H=\frac{20z+3}{21EN_{2}Tz+6EN_{2}T}$$

Divide $20z+3$ by $6N_{2}ET+21zTEN_{2}$.

$$H=\frac{20z+3}{3EN_{2}T\left(7z+2\right)}$$