Solve for x
x=\frac{17}{8}+\frac{15}{8}i=2.125+1.875i
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3\left(x-4\right)=15i-5\left(x-1\right)
Multiply both sides of the equation by 15, the least common multiple of 5,3.
3x-12=15i-5\left(x-1\right)
Use the distributive property to multiply 3 by x-4.
3x-12=15i-5x+5
Use the distributive property to multiply -5 by x-1.
3x-12+5x=15i+5
Add 5x to both sides.
8x-12=15i+5
Combine 3x and 5x to get 8x.
8x=15i+5+12
Add 12 to both sides.
8x=5+12+15i
Combine the real and imaginary parts in 15i+5+12.
8x=17+15i
Add 5 to 12.
x=\frac{17+15i}{8}
Divide both sides by 8.
x=\frac{17}{8}+\frac{15}{8}i
Divide 17+15i by 8 to get \frac{17}{8}+\frac{15}{8}i.
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