Solve x_{2}=frac{3p_{1}}{2p_{2}}*2I/5p_{1}

$$x _ { 2 } = \frac { 3 p _ { 1 } } { 2 p _ { 2 } } \cdot \frac { 2 I } { 5 p _ { 1 } }$$

Solve for I

$$I=\frac{5p_{2}x_{2}}{3}$$

$$p_{2}\neq 0\text{ and }p_{1}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10p_{1}p_{2}, the least common multiple of 2p_{2},5p_{1}.

$$x_{2}\times 10p_{1}p_{2}=5p_{1}\times 3p_{1}\times \frac{2I}{5p_{1}}$$

Multiply p_{1} and p_{1} to get p_{1}^{2}.

$$x_{2}\times 10p_{1}p_{2}=5p_{1}^{2}\times 3\times \frac{2I}{5p_{1}}$$

Multiply 5 and 3 to get 15.

$$x_{2}\times 10p_{1}p_{2}=15p_{1}^{2}\times \frac{2I}{5p_{1}}$$

Express 15\times \frac{2I}{5p_{1}} as a single fraction.

$$x_{2}\times 10p_{1}p_{2}=\frac{15\times 2I}{5p_{1}}p_{1}^{2}$$

Cancel out 5 in both numerator and denominator.

$$x_{2}\times 10p_{1}p_{2}=\frac{2\times 3I}{p_{1}}p_{1}^{2}$$

Multiply 2 and 3 to get 6.

$$x_{2}\times 10p_{1}p_{2}=\frac{6I}{p_{1}}p_{1}^{2}$$

Express \frac{6I}{p_{1}}p_{1}^{2} as a single fraction.

$$x_{2}\times 10p_{1}p_{2}=\frac{6Ip_{1}^{2}}{p_{1}}$$

Cancel out p_{1} in both numerator and denominator.

$$x_{2}\times 10p_{1}p_{2}=6Ip_{1}$$

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

$$6Ip_{1}=x_{2}\times 10p_{1}p_{2}$$

The equation is in standard form.

$$6p_{1}I=10p_{1}p_{2}x_{2}$$

Divide both sides by 6p_{1}.

$$\frac{6p_{1}I}{6p_{1}}=\frac{10p_{1}p_{2}x_{2}}{6p_{1}}$$

Dividing by 6p_{1} undoes the multiplication by 6p_{1}.

$$I=\frac{10p_{1}p_{2}x_{2}}{6p_{1}}$$

Divide 10x_{2}p_{1}p_{2} by 6p_{1}.

$$I=\frac{5p_{2}x_{2}}{3}$$

Solve for p_1

$$p_{1}\neq 0$$

$$\left(x_{2}=0\text{ and }I=0\text{ and }p_{2}\neq 0\right)\text{ or }\left(p_{2}=\frac{3I}{5x_{2}}\text{ and }x_{2}\neq 0\text{ and }I\neq 0\right)$$