Solve f^8P_{5}=7p_{5}+K^7P_{4}

$$f ^ { 8 } P _ { 5 } = 7 p _ { 5 } + K ^ { 7 } P _ { 4 }$$

Solve for K

$$K=-\frac{p_{5}}{120}+8f$$

Steps for Solving Linear Equation

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

$$7p_{5}+Kpermutation(7,4)=fpermutation(8,5)$$

Subtract 7p_{5} from both sides.

$$Kpermutation(7,4)=fpermutation(8,5)-7p_{5}$$

The equation is in standard form.

$$840K=6720f-7p_{5}$$

Divide both sides by 840.

$$\frac{840K}{840}=\frac{6720f-7p_{5}}{840}$$

Dividing by 840 undoes the multiplication by 840.

$$K=\frac{6720f-7p_{5}}{840}$$

Divide 6720f-7p_{5} by 840.

$$K=-\frac{p_{5}}{120}+8f$$

Solve for f

$$f=\frac{p_{5}+120K}{960}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$6720f=7p_{5}+840K$$

Divide both sides by 6720.

$$\frac{6720f}{6720}=\frac{7p_{5}+840K}{6720}$$

Dividing by 6720 undoes the multiplication by 6720.

$$f=\frac{7p_{5}+840K}{6720}$$

Divide 7p_{5}+840K by 6720.

$$f=\frac{K}{8}+\frac{p_{5}}{960}$$