Solve 7(18-x)-6(3-3x)=-(7x+9)-3(2x+5)-12

$$7 ( 18 - x ) - 6 ( 3 - 3 x ) = - ( 7 x + 9 ) - 3 ( 2 x + 5 ) - 12$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 18-x.

$$126-7x-6\left(3-3x\right)=-\left(7x+9\right)-3\left(2x+5\right)-12$$

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

$$126-7x-18+18x=-\left(7x+9\right)-3\left(2x+5\right)-12$$

Subtract 18 from 126 to get 108.

$$108-7x+18x=-\left(7x+9\right)-3\left(2x+5\right)-12$$

Combine -7x and 18x to get 11x.

$$108+11x=-\left(7x+9\right)-3\left(2x+5\right)-12$$

To find the opposite of 7x+9, find the opposite of each term.

$$108+11x=-7x-9-3\left(2x+5\right)-12$$

Use the distributive property to multiply -3 by 2x+5.

$$108+11x=-7x-9-6x-15-12$$

Combine -7x and -6x to get -13x.

$$108+11x=-13x-9-15-12$$

Subtract 15 from -9 to get -24.

$$108+11x=-13x-24-12$$

Subtract 12 from -24 to get -36.

$$108+11x=-13x-36$$

Add 13x to both sides.

$$108+11x+13x=-36$$

Combine 11x and 13x to get 24x.

$$108+24x=-36$$

Subtract 108 from both sides.

$$24x=-36-108$$

Subtract 108 from -36 to get -144.

$$24x=-144$$

Divide both sides by 24.

$$x=\frac{-144}{24}$$

Divide -144 by 24 to get -6.

$$x=-6$$