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Simplifying (px + q)(rx + s) = 0 Multiply (px + q) * (rx + s) (px(rx + s) + q(rx + s)) = 0 ((rx * px + s * px) + q(rx + s)) = 0 ((prx2 + psx) + q(rx + s)) = 0 (prx2 + psx + (rx * q + s * q)) = 0 (prx2 + psx + (qrx + qs)) = 0 (prx2 + psx + qrx + qs) = 0 Solving prx2 + psx + qrx + qs = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1qrx' to each side of the equation. prx2 + psx + qrx + -1qrx + qs = 0 + -1qrx Combine like terms: qrx + -1qrx = 0 prx2 + psx + 0 + qs = 0 + -1qrx prx2 + psx + qs = 0 + -1qrx Remove the zero: prx2 + psx + qs = -1qrx Add '-1qs' to each side of the equation. prx2 + psx + qs + -1qs = -1qrx + -1qs Combine like terms: qs + -1qs = 0 prx2 + psx + 0 = -1qrx + -1qs prx2 + psx = -1qrx + -1qs Reorder the terms: prx2 + psx + qrx + qs = -1qrx + qrx + -1qs + qs Combine like terms: -1qrx + qrx = 0 prx2 + psx + qrx + qs = 0 + -1qs + qs prx2 + psx + qrx + qs = -1qs + qs Combine like terms: -1qs + qs = 0 prx2 + psx + qrx + qs = 0 The solution to this equation could not be determined.
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