Solve for x
x=\frac{2}{15}\approx 0.133333333
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\left(x+2\right)\left(3x+1\right)=\left(3x-2\right)\left(x-2\right)
Variable x cannot be equal to any of the values -2,\frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by \left(3x-2\right)\left(x+2\right), the least common multiple of 3x-2,x+2.
3x^{2}+7x+2=\left(3x-2\right)\left(x-2\right)
Use the distributive property to multiply x+2 by 3x+1 and combine like terms.
3x^{2}+7x+2=3x^{2}-8x+4
Use the distributive property to multiply 3x-2 by x-2 and combine like terms.
3x^{2}+7x+2-3x^{2}=-8x+4
Subtract 3x^{2} from both sides.
7x+2=-8x+4
Combine 3x^{2} and -3x^{2} to get 0.
7x+2+8x=4
Add 8x to both sides.
15x+2=4
Combine 7x and 8x to get 15x.
15x=4-2
Subtract 2 from both sides.
15x=2
Subtract 2 from 4 to get 2.
x=\frac{2}{15}
Divide both sides by 15.
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