Solve 5[3x+2x-10]-{3x+4[3x+3x-15-(x-5)+2]}=0

$$5 [ 3 x + 2 x - 10 ] - \{ 3 x + 4 [ 3 x + 3 x - 15 - ( x - 5 ) + 2 ] \} = 0$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Combine 3x and 2x to get 5x.

$$5\left(5x-10\right)-\left(3x+4\left(3x+3x-15-\left(x-5\right)+2\right)\right)=0$$

Use the distributive property to multiply 5 by 5x-10.

$$25x-50-\left(3x+4\left(3x+3x-15-\left(x-5\right)+2\right)\right)=0$$

Combine 3x and 3x to get 6x.

$$25x-50-\left(3x+4\left(6x-15-\left(x-5\right)+2\right)\right)=0$$

To find the opposite of x-5, find the opposite of each term.

$$25x-50-\left(3x+4\left(6x-15-x-\left(-5\right)+2\right)\right)=0$$

The opposite of -5 is 5.

$$25x-50-\left(3x+4\left(6x-15-x+5+2\right)\right)=0$$

Combine 6x and -x to get 5x.

$$25x-50-\left(3x+4\left(5x-15+5+2\right)\right)=0$$

Add -15 and 5 to get -10.

$$25x-50-\left(3x+4\left(5x-10+2\right)\right)=0$$

Add -10 and 2 to get -8.

$$25x-50-\left(3x+4\left(5x-8\right)\right)=0$$

Use the distributive property to multiply 4 by 5x-8.

$$25x-50-\left(3x+20x-32\right)=0$$

Combine 3x and 20x to get 23x.

$$25x-50-\left(23x-32\right)=0$$

To find the opposite of 23x-32, find the opposite of each term.

$$25x-50-23x-\left(-32\right)=0$$

The opposite of -32 is 32.

$$25x-50-23x+32=0$$

Combine 25x and -23x to get 2x.

$$2x-50+32=0$$

Add -50 and 32 to get -18.

$$2x-18=0$$

Add 18 to both sides. Anything plus zero gives itself.

$$2x=18$$

Divide both sides by 2.

$$x=\frac{18}{2}$$

Divide 18 by 2 to get 9.

$$x=9$$