Solve 3*[2x-4*(x+3)]-5x=2+2*[(3x-1)-(6x-2)]

$$3 \cdot [ 2 x - 4 \cdot ( x + 3 ) ] - 5 x = 2 + 2 \cdot [ ( 3 x - 1 ) - ( 6 x - 2 ) ]$$

Solve for x

$$x=-8$$

Steps for Solving Linear Equation

Use the distributive property to multiply -4 by x+3.

$$3\left(2x-4x-12\right)-5x=2+2\left(3x-1-\left(6x-2\right)\right)$$

Combine 2x and -4x to get -2x.

$$3\left(-2x-12\right)-5x=2+2\left(3x-1-\left(6x-2\right)\right)$$

Use the distributive property to multiply 3 by -2x-12.

$$-6x-36-5x=2+2\left(3x-1-\left(6x-2\right)\right)$$

Combine -6x and -5x to get -11x.

$$-11x-36=2+2\left(3x-1-\left(6x-2\right)\right)$$

To find the opposite of 6x-2, find the opposite of each term.

$$-11x-36=2+2\left(3x-1-6x-\left(-2\right)\right)$$

The opposite of -2 is 2.

$$-11x-36=2+2\left(3x-1-6x+2\right)$$

Combine 3x and -6x to get -3x.

$$-11x-36=2+2\left(-3x-1+2\right)$$

Add -1 and 2 to get 1.

$$-11x-36=2+2\left(-3x+1\right)$$

Use the distributive property to multiply 2 by -3x+1.

$$-11x-36=2-6x+2$$

Add 2 and 2 to get 4.

$$-11x-36=4-6x$$

Add 6x to both sides.

$$-11x-36+6x=4$$

Combine -11x and 6x to get -5x.

$$-5x-36=4$$

Add 36 to both sides.

$$-5x=4+36$$

Add 4 and 36 to get 40.

$$-5x=40$$

Divide both sides by -5.

$$x=\frac{40}{-5}$$

Divide 40 by -5 to get -8.

$$x=-8$$