Solve 7(2x+4(x+2y+5))=12(3x+6y+B)

$$7 ( 2 x + 4 ( x + 2 y + 5 ) ) = 12 ( 3 x + 6 y + B )$$

Solve for B

$$B=\frac{x}{2}-\frac{4y}{3}+\frac{35}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by x+2y+5.

$$7\left(2x+4x+8y+20\right)=12\left(3x+6y+B\right)$$

Combine 2x and 4x to get 6x.

$$7\left(6x+8y+20\right)=12\left(3x+6y+B\right)$$

Use the distributive property to multiply 7 by 6x+8y+20.

$$42x+56y+140=12\left(3x+6y+B\right)$$

Use the distributive property to multiply 12 by 3x+6y+B.

$$42x+56y+140=36x+72y+12B$$

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

$$36x+72y+12B=42x+56y+140$$

Subtract 36x from both sides.

$$72y+12B=42x+56y+140-36x$$

Combine 42x and -36x to get 6x.

$$72y+12B=6x+56y+140$$

Subtract 72y from both sides.

$$12B=6x+56y+140-72y$$

Combine 56y and -72y to get -16y.

$$12B=6x-16y+140$$

Divide both sides by 12.

$$\frac{12B}{12}=\frac{6x-16y+140}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$B=\frac{6x-16y+140}{12}$$

Divide 6x-16y+140 by 12.

$$B=\frac{x}{2}-\frac{4y}{3}+\frac{35}{3}$$

Solve for x

$$x=\frac{8y}{3}+2B-\frac{70}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by x+2y+5.

$$7\left(2x+4x+8y+20\right)=12\left(3x+6y+B\right)$$

Combine 2x and 4x to get 6x.

$$7\left(6x+8y+20\right)=12\left(3x+6y+B\right)$$

Use the distributive property to multiply 7 by 6x+8y+20.

$$42x+56y+140=12\left(3x+6y+B\right)$$

Use the distributive property to multiply 12 by 3x+6y+B.

$$42x+56y+140=36x+72y+12B$$

Subtract 36x from both sides.

$$42x+56y+140-36x=72y+12B$$

Combine 42x and -36x to get 6x.

$$6x+56y+140=72y+12B$$

Subtract 56y from both sides.

$$6x+140=72y+12B-56y$$

Combine 72y and -56y to get 16y.

$$6x+140=16y+12B$$

Subtract 140 from both sides.

$$6x=16y+12B-140$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{16y+12B-140}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{16y+12B-140}{6}$$

Divide 16y+12B-140 by 6.

$$x=\frac{8y}{3}+2B-\frac{70}{3}$$