Solve 2a+(4a+2)b=b-10a

$$2 a + ( 4 a + 2 ) b = b - 10 a$$

Solve for a

$$a=-\frac{b}{4\left(b+3\right)}$$

$$b\neq -3$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4a+2 by b.

$$2a+4ab+2b=b-10a$$

Add 10a to both sides.

$$2a+4ab+2b+10a=b$$

Combine 2a and 10a to get 12a.

$$12a+4ab+2b=b$$

Subtract 2b from both sides.

$$12a+4ab=b-2b$$

Combine b and -2b to get -b.

$$12a+4ab=-b$$

Combine all terms containing a.

$$\left(12+4b\right)a=-b$$

The equation is in standard form.

$$\left(4b+12\right)a=-b$$

Divide both sides by 4b+12.

$$\frac{\left(4b+12\right)a}{4b+12}=-\frac{b}{4b+12}$$

Dividing by 4b+12 undoes the multiplication by 4b+12.

$$a=-\frac{b}{4b+12}$$

Divide -b by 4b+12.

$$a=-\frac{b}{4\left(b+3\right)}$$

Solve for b

$$b=-\frac{12a}{4a+1}$$

$$a\neq -\frac{1}{4}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4a+2 by b.

$$2a+4ab+2b=b-10a$$

Subtract b from both sides.

$$2a+4ab+2b-b=-10a$$

Combine 2b and -b to get b.

$$2a+4ab+b=-10a$$

Subtract 2a from both sides.

$$4ab+b=-10a-2a$$

Combine -10a and -2a to get -12a.

$$4ab+b=-12a$$

Combine all terms containing b.

$$\left(4a+1\right)b=-12a$$

Divide both sides by 4a+1.

$$\frac{\left(4a+1\right)b}{4a+1}=-\frac{12a}{4a+1}$$

Dividing by 4a+1 undoes the multiplication by 4a+1.

$$b=-\frac{12a}{4a+1}$$