# Solve for y 3*(12yi)=27+36i 3⋅(12yi)=27+36i
Multiply 12 by 3.
36⋅(yi)=27+36i
Divide each term by 36i and simplify.
Divide each term in 36⋅(yi)=27+36i by 36i.
36⋅(yi)36i=2736i+36i36i
Simplify 36⋅(yi)36i.
Cancel the common factor of 36.
Cancel the common factor.
36⋅(yi)36i=2736i+36i36i
Rewrite the expression.
yii=2736i+36i36i
yii=2736i+36i36i
Cancel the common factor of i.
Cancel the common factor.
yii=2736i+36i36i
Divide y by 1.
y=2736i+36i36i
y=2736i+36i36i
y=2736i+36i36i
Simplify 2736i+36i36i.
Simplify each term.
Cancel the common factor of 27 and 36.
Factor 9 out of 27.
y=9(3)36i+36i36i
Cancel the common factors.
Factor 9 out of 36i.
y=9(3)9(4i)+36i36i
Cancel the common factor.
y=9⋅39(4i)+36i36i
Rewrite the expression.
y=34i+36i36i
y=34i+36i36i
y=34i+36i36i
Multiply the numerator and denominator of 34i by the conjugate of 4i to make the denominator real.
y=34i⋅ii+36i36i
Multiply.
Combine.
y=3i4ii+36i36i
Simplify the denominator.
y=3i4(ii)+36i36i
Raise i to the power of 1.
y=3i4(i1i)+36i36i
Raise i to the power of 1.
y=3i4(i1i1)+36i36i
Use the power rule aman=am+n to combine exponents.
y=3i4i1+1+36i36i
Add 1 and 1.
y=3i4i2+36i36i
Rewrite i2 as -1.
y=3i4⋅-1+36i36i
y=3i4⋅-1+36i36i
y=3i4⋅-1+36i36i
Multiply 4 by -1.
y=3i-4+36i36i
Move the negative in front of the fraction.
y=-3i4+36i36i
Cancel the common factor of 36.
Cancel the common factor.
y=-3i4+36i36i
Rewrite the expression.
y=-3i4+ii
y=-3i4+ii
Cancel the common factor of i.
Cancel the common factor.
y=-3i4+ii
Divide 1 by 1.
y=-3i4+1
y=-3i4+1
y=-3i4+1
Reorder -3i4 and 1.
y=1-3i4
y=1-3i4
y=1-3i4
Solve for y 3*(12yi)=27+36i

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