Solve for x
x = -\frac{11}{9} = -1\frac{2}{9} \approx -1.222222222
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\left(2x+3\right)\left(6x+7\right)=\left(3x+2\right)\left(4x+5\right)
Variable x cannot be equal to any of the values -\frac{3}{2},-\frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by \left(2x+3\right)\left(3x+2\right), the least common multiple of 3x+2,2x+3.
12x^{2}+32x+21=\left(3x+2\right)\left(4x+5\right)
Use the distributive property to multiply 2x+3 by 6x+7 and combine like terms.
12x^{2}+32x+21=12x^{2}+23x+10
Use the distributive property to multiply 3x+2 by 4x+5 and combine like terms.
12x^{2}+32x+21-12x^{2}=23x+10
Subtract 12x^{2} from both sides.
32x+21=23x+10
Combine 12x^{2} and -12x^{2} to get 0.
32x+21-23x=10
Subtract 23x from both sides.
9x+21=10
Combine 32x and -23x to get 9x.
9x=10-21
Subtract 21 from both sides.
9x=-11
Subtract 21 from 10 to get -11.
x=\frac{-11}{9}
Divide both sides by 9.
x=-\frac{11}{9}
Fraction \frac{-11}{9} can be rewritten as -\frac{11}{9} by extracting the negative sign.
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