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42\left(x-2\right)-28\left(-2x+3\right)+14=2\left(13x+7\right)-12x
Multiply both sides of the equation by 14, the least common multiple of 7,14.
42x-84-28\left(-2x+3\right)+14=2\left(13x+7\right)-12x
Use the distributive property to multiply 42 by x-2.
42x-84+56x-84+14=2\left(13x+7\right)-12x
Use the distributive property to multiply -28 by -2x+3.
98x-84-84+14=2\left(13x+7\right)-12x
Combine 42x and 56x to get 98x.
98x-168+14=2\left(13x+7\right)-12x
Subtract 84 from -84 to get -168.
98x-154=2\left(13x+7\right)-12x
Add -168 and 14 to get -154.
98x-154=26x+14-12x
Use the distributive property to multiply 2 by 13x+7.
98x-154=14x+14
Combine 26x and -12x to get 14x.
98x-154-14x=14
Subtract 14x from both sides.
84x-154=14
Combine 98x and -14x to get 84x.
84x=14+154
Add 154 to both sides.
84x=168
Add 14 and 154 to get 168.
x=\frac{168}{84}
Divide both sides by 84.
x=2
Divide 168 by 84 to get 2.