Solve b^3 (a-5)i=a 8i

Evaluate

b^{3} (a - 5) i = a \times 8 i

Use the commutative property to reorder the terms

i b^{3} (a - 5) = a \times 8 i

Multiply the terms

More Steps

i b^{3} (a - 5) = 8 ia

Expand the expression

More Steps

i b^{3} a - 5 i b^{3} = 8 ia

Move the expression to the left side

i b^{3} a - 5 i b^{3} - 8 ia = 0

Rewrite the expression

0 + (b^{3} a - 5 b^{3} - 8 a) i = 0

Rewrite the expression

{0 = 0 b^{3} a - 5 b^{3} - 8 a = 0

Rearrange the terms

b^{3} a - 5 b^{3} - 8 a = 0

Collect like terms by calculating the sum or difference of their coefficients

(b^{3} - 8) a - 5 b^{3} = 0

Move the constant to the right side

(b^{3} - 8) a = 0 + 5 b^{3}

Removing 0 doesn't change the value,so remove it from the expression

(b^{3} - 8) a = 5 b^{3}

Divide both sides

\frac{( b ^{3} - 8 ) a}{b ^{3} - 8} = \frac{5 b ^{3}}{b ^{3} - 8}

Divide the numbers

a = \frac{5 b ^{3}}{b ^{3} - 8}

Solution

(a, b) = (\frac{5 b ^{3}}{b ^{3} - 8}, b), b \in R

Alternative Form

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