Solve 6(2x+3)-5(4x-1)=2(3x-7)+3(5x-7)

$$6 ( 2 x + 3 ) - 5 ( 4 x - 1 ) = 2 ( 3 x - 7 ) + 3 ( 5 x - 7 )$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by 2x+3.

$$12x+18-5\left(4x-1\right)=2\left(3x-7\right)+3\left(5x-7\right)$$

Use the distributive property to multiply -5 by 4x-1.

$$12x+18-20x+5=2\left(3x-7\right)+3\left(5x-7\right)$$

Combine 12x and -20x to get -8x.

$$-8x+18+5=2\left(3x-7\right)+3\left(5x-7\right)$$

Add 18 and 5 to get 23.

$$-8x+23=2\left(3x-7\right)+3\left(5x-7\right)$$

Use the distributive property to multiply 2 by 3x-7.

$$-8x+23=6x-14+3\left(5x-7\right)$$

Use the distributive property to multiply 3 by 5x-7.

$$-8x+23=6x-14+15x-21$$

Combine 6x and 15x to get 21x.

$$-8x+23=21x-14-21$$

Subtract 21 from -14 to get -35.

$$-8x+23=21x-35$$

Subtract 21x from both sides.

$$-8x+23-21x=-35$$

Combine -8x and -21x to get -29x.

$$-29x+23=-35$$

Subtract 23 from both sides.

$$-29x=-35-23$$

Subtract 23 from -35 to get -58.

$$-29x=-58$$

Divide both sides by -29.

$$x=\frac{-58}{-29}$$

Divide -58 by -29 to get 2.

$$x=2$$