Solve 4y+1=b+12mx-15m+12x-15

$$4 y + 1 = b + 12 m x - 15 m + 12 x - 15$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{12x-4y+b-16}{3\left(4x-5\right)}\text{, }&x\neq \frac{5}{4}\\m\in \mathrm{C}\text{, }&y=\frac{b-1}{4}\text{ and }x=\frac{5}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$b+12mx-15m+12x-15=4y+1$$

Subtract b from both sides.

$$12mx-15m+12x-15=4y+1-b$$

Subtract 12x from both sides.

$$12mx-15m-15=4y+1-b-12x$$

Add 15 to both sides.

$$12mx-15m=4y+1-b-12x+15$$

Add 1 and 15 to get 16.

$$12mx-15m=4y+16-b-12x$$

Combine all terms containing m.

$$\left(12x-15\right)m=4y+16-b-12x$$

The equation is in standard form.

$$\left(12x-15\right)m=16-b+4y-12x$$

Divide both sides by 12x-15.

$$\frac{\left(12x-15\right)m}{12x-15}=\frac{16-b+4y-12x}{12x-15}$$

Dividing by 12x-15 undoes the multiplication by 12x-15.

$$m=\frac{16-b+4y-12x}{12x-15}$$

Divide 4y+16-b-12x by 12x-15.

$$m=\frac{16-b+4y-12x}{3\left(4x-5\right)}$$

Solve for b

$$b=16+15m+4y-12x-12mx$$

Solution Steps

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

$$b+12mx-15m+12x-15=4y+1$$

Subtract 12mx from both sides.

$$b-15m+12x-15=4y+1-12mx$$

Add 15m to both sides.

$$b+12x-15=4y+1-12mx+15m$$

Subtract 12x from both sides.

$$b-15=4y+1-12mx+15m-12x$$

Add 15 to both sides.

$$b=4y+1-12mx+15m-12x+15$$

Add 1 and 15 to get 16.

$$b=4y+16-12mx+15m-12x$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{12x-4y+b-16}{3\left(4x-5\right)}\text{, }&x\neq \frac{5}{4}\\m\in \mathrm{R}\text{, }&y=\frac{b-1}{4}\text{ and }x=\frac{5}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$b+12mx-15m+12x-15=4y+1$$

Subtract b from both sides.

$$12mx-15m+12x-15=4y+1-b$$

Subtract 12x from both sides.

$$12mx-15m-15=4y+1-b-12x$$

Add 15 to both sides.

$$12mx-15m=4y+1-b-12x+15$$

Add 1 and 15 to get 16.

$$12mx-15m=4y+16-b-12x$$

Combine all terms containing m.

$$\left(12x-15\right)m=4y+16-b-12x$$

The equation is in standard form.

$$\left(12x-15\right)m=16-b+4y-12x$$

Divide both sides by 12x-15.

$$\frac{\left(12x-15\right)m}{12x-15}=\frac{16-b+4y-12x}{12x-15}$$

Dividing by 12x-15 undoes the multiplication by 12x-15.

$$m=\frac{16-b+4y-12x}{12x-15}$$

Divide 4y+16-b-12x by 12x-15.

$$m=\frac{16-b+4y-12x}{3\left(4x-5\right)}$$