Solve 3x=(4x-3)(m+6)

$$3 x = ( 4 x - 3 ) ( m + 6 )$$

Solve for m

$$m=-\frac{3\left(6-7x\right)}{3-4x}$$

$$x\neq \frac{3}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4x-3 by m+6.

$$3x=4xm+24x-3m-18$$

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

$$4xm+24x-3m-18=3x$$

Subtract 24x from both sides.

$$4xm-3m-18=3x-24x$$

Combine 3x and -24x to get -21x.

$$4xm-3m-18=-21x$$

Add 18 to both sides.

$$4xm-3m=-21x+18$$

Combine all terms containing m.

$$\left(4x-3\right)m=-21x+18$$

The equation is in standard form.

$$\left(4x-3\right)m=18-21x$$

Divide both sides by 4x-3.

$$\frac{\left(4x-3\right)m}{4x-3}=\frac{18-21x}{4x-3}$$

Dividing by 4x-3 undoes the multiplication by 4x-3.

$$m=\frac{18-21x}{4x-3}$$

Divide -21x+18 by 4x-3.

$$m=\frac{3\left(6-7x\right)}{4x-3}$$

Solve for x

$$x=\frac{3\left(m+6\right)}{4m+21}$$

$$m\neq -\frac{21}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4x-3 by m+6.

$$3x=4xm+24x-3m-18$$

Subtract 4xm from both sides.

$$3x-4xm=24x-3m-18$$

Subtract 24x from both sides.

$$3x-4xm-24x=-3m-18$$

Combine 3x and -24x to get -21x.

$$-21x-4xm=-3m-18$$

Combine all terms containing x.

$$\left(-21-4m\right)x=-3m-18$$

The equation is in standard form.

$$\left(-4m-21\right)x=-3m-18$$

Divide both sides by -21-4m.

$$\frac{\left(-4m-21\right)x}{-4m-21}=\frac{-3m-18}{-4m-21}$$

Dividing by -21-4m undoes the multiplication by -21-4m.

$$x=\frac{-3m-18}{-4m-21}$$

Divide -3m-18 by -21-4m.

$$x=\frac{3\left(m+6\right)}{4m+21}$$