Solve (3x-1)(x+2)/3-2x^2+1/2=13/6

$$\frac{ (3x-1)(x+2) }{ 3 } - \frac{ 2 { x }^{ 2 } +1 }{ 2 } = \frac{ 13 }{ 6 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2,6.

$$2\left(3x-1\right)\left(x+2\right)-3\left(2x^{2}+1\right)=13$$

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

$$\left(6x-2\right)\left(x+2\right)-3\left(2x^{2}+1\right)=13$$

Use the distributive property to multiply 6x-2 by x+2 and combine like terms.

$$6x^{2}+10x-4-3\left(2x^{2}+1\right)=13$$

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

$$6x^{2}+10x-4-6x^{2}-3=13$$

Combine 6x^{2} and -6x^{2} to get 0.

$$10x-4-3=13$$

Subtract 3 from -4 to get -7.

$$10x-7=13$$

Add 7 to both sides.

$$10x=13+7$$

Add 13 and 7 to get 20.

$$10x=20$$

Divide both sides by 10.

$$x=\frac{20}{10}$$

Divide 20 by 10 to get 2.

$$x=2$$