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Simplifying g(x) = 0.5(2x + 10)(x + -3) Multiply g * x gx = 0.5(2x + 10)(x + -3) Reorder the terms: gx = 0.5(10 + 2x)(x + -3) Reorder the terms: gx = 0.5(10 + 2x)(-3 + x) Multiply (10 + 2x) * (-3 + x) gx = 0.5(10(-3 + x) + 2x * (-3 + x)) gx = 0.5((-3 * 10 + x * 10) + 2x * (-3 + x)) gx = 0.5((-30 + 10x) + 2x * (-3 + x)) gx = 0.5(-30 + 10x + (-3 * 2x + x * 2x)) gx = 0.5(-30 + 10x + (-6x + 2x2)) Combine like terms: 10x + -6x = 4x gx = 0.5(-30 + 4x + 2x2) gx = (-30 * 0.5 + 4x * 0.5 + 2x2 * 0.5) gx = (-15 + 2x + 1x2) Solving gx = -15 + 2x + 1x2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Divide each side by 'x'. g = -15x-1 + 2 + x Simplifying g = -15x-1 + 2 + x Reorder the terms: g = 2 + -15x-1 + x
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