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Simplifying 12x2 + -18x + 24(a + 5) = 0 Reorder the terms: 12x2 + -18x + 24(5 + a) = 0 12x2 + -18x + (5 * 24 + a * 24) = 0 12x2 + -18x + (120 + 24a) = 0 Reorder the terms: 120 + 24a + -18x + 12x2 = 0 Solving 120 + 24a + -18x + 12x2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + 24a + -18x + -120 + 12x2 = 0 + -120 Reorder the terms: 120 + -120 + 24a + -18x + 12x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 24a + -18x + 12x2 = 0 + -120 24a + -18x + 12x2 = 0 + -120 Combine like terms: 0 + -120 = -120 24a + -18x + 12x2 = -120 Add '18x' to each side of the equation. 24a + -18x + 18x + 12x2 = -120 + 18x Combine like terms: -18x + 18x = 0 24a + 0 + 12x2 = -120 + 18x 24a + 12x2 = -120 + 18x Add '-12x2' to each side of the equation. 24a + 12x2 + -12x2 = -120 + 18x + -12x2 Combine like terms: 12x2 + -12x2 = 0 24a + 0 = -120 + 18x + -12x2 24a = -120 + 18x + -12x2 Divide each side by '24'. a = -5 + 0.75x + -0.5x2 Simplifying a = -5 + 0.75x + -0.5x2
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