Solve Q_{1}=600-4P_{A}-003M-12P_{A}+15G+6P_{B}+15N

$$Q _ { 1 } = 600 - 4 P _ { A } - 003 M - 12 P _ { A } + 15 G + 6 P _ { B } + 15 N$$

Solve for G

$$G=\frac{-15N+16P_{A}-6P_{B}+Q_{1}-600}{15}$$

Steps for Solving Linear Equation

Multiply 0 and 0 to get 0.

$$Q_{1}=600-4P_{A}-0\times 3M-12P_{A}+15G+6P_{B}+15N$$

Multiply 0 and 3 to get 0.

$$Q_{1}=600-4P_{A}-0M-12P_{A}+15G+6P_{B}+15N$$

Anything times zero gives zero.

$$Q_{1}=600-4P_{A}-0-12P_{A}+15G+6P_{B}+15N$$

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

$$600-4P_{A}-0-12P_{A}+15G+6P_{B}+15N=Q_{1}$$

Subtract 600-4P_{A}-0 from both sides.

$$-12P_{A}+15G+6P_{B}+15N=Q_{1}-\left(600-4P_{A}-0\right)$$

Add 12P_{A} to both sides.

$$15G+6P_{B}+15N=Q_{1}-\left(600-4P_{A}-0\right)+12P_{A}$$

Subtract 6P_{B} from both sides.

$$15G+15N=Q_{1}-\left(600-4P_{A}-0\right)+12P_{A}-6P_{B}$$

Subtract 15N from both sides.

$$15G=Q_{1}-\left(600-4P_{A}-0\right)+12P_{A}-6P_{B}-15N$$

Reorder the terms.

$$15G=Q_{1}-\left(-4P_{A}+600\right)-15N-6P_{B}+12P_{A}$$

To find the opposite of -4P_{A}+600, find the opposite of each term.

$$15G=Q_{1}+4P_{A}-600-15N-6P_{B}+12P_{A}$$

Combine 4P_{A} and 12P_{A} to get 16P_{A}.

$$15G=Q_{1}+16P_{A}-600-15N-6P_{B}$$

The equation is in standard form.

$$15G=-15N+16P_{A}-6P_{B}+Q_{1}-600$$

Divide both sides by 15.

$$\frac{15G}{15}=\frac{-15N+16P_{A}-6P_{B}+Q_{1}-600}{15}$$

Dividing by 15 undoes the multiplication by 15.

$$G=\frac{-15N+16P_{A}-6P_{B}+Q_{1}-600}{15}$$

Divide Q_{1}+16P_{A}-600-15N-6P_{B} by 15.

$$G=\frac{Q_{1}}{15}+\frac{16P_{A}}{15}-\frac{2P_{B}}{5}-N-40$$

Solve for M (complex solution)

$$M\in \mathrm{C}$$

$$Q_{1}=15G+15N-16P_{A}+6P_{B}+600$$

Solve for M

$$M\in \mathrm{R}$$

$$Q_{1}=15G+15N-16P_{A}+6P_{B}+600$$