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Simplifying 15(w + -3) = 20w + 12(2w + 1) Reorder the terms: 15(-3 + w) = 20w + 12(2w + 1) (-3 * 15 + w * 15) = 20w + 12(2w + 1) (-45 + 15w) = 20w + 12(2w + 1) Reorder the terms: -45 + 15w = 20w + 12(1 + 2w) -45 + 15w = 20w + (1 * 12 + 2w * 12) -45 + 15w = 20w + (12 + 24w) Reorder the terms: -45 + 15w = 12 + 20w + 24w Combine like terms: 20w + 24w = 44w -45 + 15w = 12 + 44w Solving -45 + 15w = 12 + 44w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-44w' to each side of the equation. -45 + 15w + -44w = 12 + 44w + -44w Combine like terms: 15w + -44w = -29w -45 + -29w = 12 + 44w + -44w Combine like terms: 44w + -44w = 0 -45 + -29w = 12 + 0 -45 + -29w = 12 Add '45' to each side of the equation. -45 + 45 + -29w = 12 + 45 Combine like terms: -45 + 45 = 0 0 + -29w = 12 + 45 -29w = 12 + 45 Combine like terms: 12 + 45 = 57 -29w = 57 Divide each side by '-29'. w = -1.965517241 Simplifying w = -1.965517241
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