Solve (2a+4b)(c-6d)=4e+2

$$( 2 a + 4 b ) ( c - 6 d ) = 4 e + 2$$

Solve for a

$$a=-\frac{2bc-12bd-2e-1}{c-6d}$$

$$c\neq 6d$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2a+4b by c-6d.

$$2ac-12da+4bc-24db=4e+2$$

Subtract 4bc from both sides.

$$2ac-12da-24db=4e+2-4bc$$

Add 24db to both sides.

$$2ac-12da=4e+2-4bc+24db$$

Combine all terms containing a.

$$\left(2c-12d\right)a=4e+2-4bc+24db$$

The equation is in standard form.

$$\left(2c-12d\right)a=2+4e+24bd-4bc$$

Divide both sides by 2c-12d.

$$\frac{\left(2c-12d\right)a}{2c-12d}=\frac{2+4e+24bd-4bc}{2c-12d}$$

Dividing by 2c-12d undoes the multiplication by 2c-12d.

$$a=\frac{2+4e+24bd-4bc}{2c-12d}$$

Divide 4e+2-4bc+24db by 2c-12d.

$$a=\frac{1+2e+12bd-2bc}{c-6d}$$

Solve for b

$$b=-\frac{ac-6ad-2e-1}{2\left(c-6d\right)}$$

$$c\neq 6d$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2a+4b by c-6d.

$$2ac-12da+4bc-24db=4e+2$$

Subtract 2ac from both sides.

$$-12da+4bc-24db=4e+2-2ac$$

Add 12da to both sides.

$$4bc-24db=4e+2-2ac+12da$$

Combine all terms containing b.

$$\left(4c-24d\right)b=4e+2-2ac+12da$$

The equation is in standard form.

$$\left(4c-24d\right)b=2+4e+12ad-2ac$$

Divide both sides by 4c-24d.

$$\frac{\left(4c-24d\right)b}{4c-24d}=\frac{2+4e+12ad-2ac}{4c-24d}$$

Dividing by 4c-24d undoes the multiplication by 4c-24d.

$$b=\frac{2+4e+12ad-2ac}{4c-24d}$$

Divide 4e+2-2ac+12da by 4c-24d.

$$b=\frac{1+2e+6ad-ac}{2\left(c-6d\right)}$$