Example

Solving 18a230=33a18a^2 - 30 = -33a

Solve 18a230=33a18a^2 - 30 = -33a by first writing it in standard form and factoring out a constant.

Add 33a33a to both sides and arrange in descending order: 18a2+33a30=018a^2 + 33a - 30 = 0. Factor out the greatest common factor of 33: 3(6a2+11a10)=03(6a^2 + 11a - 10) = 0. Factor the resulting trinomial: 3(3a2)(2a+5)=03(3a - 2)(2a + 5) = 0. Apply the Zero Product Property. Since the constant factor 33 cannot equal zero (303 \neq 0), set the variable factors to zero: 3a2=03a - 2 = 0 or 2a+5=02a + 5 = 0. Solve the linear equations: a=23a = \frac{2}{3} and a=52a = -\frac{5}{2}.

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Updated 2026-04-30

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