ia(s^2+4s+1)+ib(-s^2-1)=-2

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Solution for ia(s^2+4s+1)+ib(-s^2-1)=-2 equation:


Simplifying
ia(s2 + 4s + 1) + ib(-1s2 + -1) = -2

Reorder the terms:
ai(1 + 4s + s2) + ib(-1s2 + -1) = -2
(1 * ai + 4s * ai + s2 * ai) + ib(-1s2 + -1) = -2
(1ai + 4ais + ais2) + ib(-1s2 + -1) = -2

Reorder the terms:
1ai + 4ais + ais2 + bi(-1 + -1s2) = -2
1ai + 4ais + ais2 + (-1 * bi + -1s2 * bi) = -2
1ai + 4ais + ais2 + (-1bi + -1bis2) = -2

Solving
1ai + 4ais + ais2 + -1bi + -1bis2 = -2

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add 'bi' to each side of the equation.
1ai + 4ais + ais2 + -1bi + bi + -1bis2 = -2 + bi

Combine like terms: -1bi + bi = 0
1ai + 4ais + ais2 + 0 + -1bis2 = -2 + bi
1ai + 4ais + ais2 + -1bis2 = -2 + bi

Add 'bis2' to each side of the equation.
1ai + 4ais + ais2 + -1bis2 + bis2 = -2 + bi + bis2

Combine like terms: -1bis2 + bis2 = 0
1ai + 4ais + ais2 + 0 = -2 + bi + bis2
1ai + 4ais + ais2 = -2 + bi + bis2

Reorder the terms:
2 + 1ai + 4ais + ais2 + -1bi + -1bis2 = -2 + bi + bis2 + 2 + -1bi + -1bis2

Reorder the terms:
2 + 1ai + 4ais + ais2 + -1bi + -1bis2 = -2 + 2 + bi + -1bi + bis2 + -1bis2

Combine like terms: -2 + 2 = 0
2 + 1ai + 4ais + ais2 + -1bi + -1bis2 = 0 + bi + -1bi + bis2 + -1bis2
2 + 1ai + 4ais + ais2 + -1bi + -1bis2 = bi + -1bi + bis2 + -1bis2

Combine like terms: bi + -1bi = 0
2 + 1ai + 4ais + ais2 + -1bi + -1bis2 = 0 + bis2 + -1bis2
2 + 1ai + 4ais + ais2 + -1bi + -1bis2 = bis2 + -1bis2

Combine like terms: bis2 + -1bis2 = 0
2 + 1ai + 4ais + ais2 + -1bi + -1bis2 = 0

The solution to this equation could not be determined.

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