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Simplifying 0.5x(x + 2) = (0.5x + 2)(x + -3) Reorder the terms: 0.5x(2 + x) = (0.5x + 2)(x + -3) (2 * 0.5x + x * 0.5x) = (0.5x + 2)(x + -3) (1x + 0.5x2) = (0.5x + 2)(x + -3) Reorder the terms: 1x + 0.5x2 = (2 + 0.5x)(x + -3) Reorder the terms: 1x + 0.5x2 = (2 + 0.5x)(-3 + x) Multiply (2 + 0.5x) * (-3 + x) 1x + 0.5x2 = (2(-3 + x) + 0.5x * (-3 + x)) 1x + 0.5x2 = ((-3 * 2 + x * 2) + 0.5x * (-3 + x)) 1x + 0.5x2 = ((-6 + 2x) + 0.5x * (-3 + x)) 1x + 0.5x2 = (-6 + 2x + (-3 * 0.5x + x * 0.5x)) 1x + 0.5x2 = (-6 + 2x + (-1.5x + 0.5x2)) Combine like terms: 2x + -1.5x = 0.5x 1x + 0.5x2 = (-6 + 0.5x + 0.5x2) Add '-0.5x2' to each side of the equation. 1x + 0.5x2 + -0.5x2 = -6 + 0.5x + 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 1x + 0.0 = -6 + 0.5x + 0.5x2 + -0.5x2 1x = -6 + 0.5x + 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 1x = -6 + 0.5x + 0.0 1x = -6 + 0.5x Solving 1x = -6 + 0.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5x' to each side of the equation. 1x + -0.5x = -6 + 0.5x + -0.5x Combine like terms: 1x + -0.5x = 0.5x 0.5x = -6 + 0.5x + -0.5x Combine like terms: 0.5x + -0.5x = 0.0 0.5x = -6 + 0.0 0.5x = -6 Divide each side by '0.5'. x = -12 Simplifying x = -12
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