Solve 65*117=(65m+117n)*x

$$65 \times 117 = ( 65 m + 117 n ) \times x$$

Solve for m

$$m=-\frac{9n}{5}+\frac{117}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply 65 and 117 to get 7605.

$$7605=\left(65m+117n\right)x$$

Use the distributive property to multiply 65m+117n by x.

$$7605=65mx+117nx$$

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

$$65mx+117nx=7605$$

Subtract 117nx from both sides.

$$65mx=7605-117nx$$

The equation is in standard form.

$$65xm=7605-117nx$$

Divide both sides by 65x.

$$\frac{65xm}{65x}=\frac{7605-117nx}{65x}$$

Dividing by 65x undoes the multiplication by 65x.

$$m=\frac{7605-117nx}{65x}$$

Divide 7605-117nx by 65x.

$$m=-\frac{9n}{5}+\frac{117}{x}$$

Solve for n

$$n=-\frac{5m}{9}+\frac{65}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply 65 and 117 to get 7605.

$$7605=\left(65m+117n\right)x$$

Use the distributive property to multiply 65m+117n by x.

$$7605=65mx+117nx$$

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

$$65mx+117nx=7605$$

Subtract 65mx from both sides.

$$117nx=7605-65mx$$

The equation is in standard form.

$$117xn=7605-65mx$$

Divide both sides by 117x.

$$\frac{117xn}{117x}=\frac{7605-65mx}{117x}$$

Dividing by 117x undoes the multiplication by 117x.

$$n=\frac{7605-65mx}{117x}$$

Divide 7605-65mx by 117x.

$$n=-\frac{5m}{9}+\frac{65}{x}$$