Solve for x
x=\frac{9}{16}=0.5625
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2\left(2x+3\right)+3\left(4x-3\right)=6
Multiply both sides of the equation by 6, the least common multiple of 3,2.
4x+6+3\left(4x-3\right)=6
Use the distributive property to multiply 2 by 2x+3.
4x+6+12x-9=6
Use the distributive property to multiply 3 by 4x-3.
16x+6-9=6
Combine 4x and 12x to get 16x.
16x-3=6
Subtract 9 from 6 to get -3.
16x=6+3
Add 3 to both sides.
16x=9
Add 6 and 3 to get 9.
x=\frac{9}{16}
Divide both sides by 16.
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