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Simplifying q(2q + -3) = (2q + 1)(q + -4) Reorder the terms: q(-3 + 2q) = (2q + 1)(q + -4) (-3 * q + 2q * q) = (2q + 1)(q + -4) (-3q + 2q2) = (2q + 1)(q + -4) Reorder the terms: -3q + 2q2 = (1 + 2q)(q + -4) Reorder the terms: -3q + 2q2 = (1 + 2q)(-4 + q) Multiply (1 + 2q) * (-4 + q) -3q + 2q2 = (1(-4 + q) + 2q * (-4 + q)) -3q + 2q2 = ((-4 * 1 + q * 1) + 2q * (-4 + q)) -3q + 2q2 = ((-4 + 1q) + 2q * (-4 + q)) -3q + 2q2 = (-4 + 1q + (-4 * 2q + q * 2q)) -3q + 2q2 = (-4 + 1q + (-8q + 2q2)) Combine like terms: 1q + -8q = -7q -3q + 2q2 = (-4 + -7q + 2q2) Add '-2q2' to each side of the equation. -3q + 2q2 + -2q2 = -4 + -7q + 2q2 + -2q2 Combine like terms: 2q2 + -2q2 = 0 -3q + 0 = -4 + -7q + 2q2 + -2q2 -3q = -4 + -7q + 2q2 + -2q2 Combine like terms: 2q2 + -2q2 = 0 -3q = -4 + -7q + 0 -3q = -4 + -7q Solving -3q = -4 + -7q Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7q' to each side of the equation. -3q + 7q = -4 + -7q + 7q Combine like terms: -3q + 7q = 4q 4q = -4 + -7q + 7q Combine like terms: -7q + 7q = 0 4q = -4 + 0 4q = -4 Divide each side by '4'. q = -1 Simplifying q = -1
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