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Simplifying (8w + 5)(5w + 7) = (4w + -3)(10w + -7) Reorder the terms: (5 + 8w)(5w + 7) = (4w + -3)(10w + -7) Reorder the terms: (5 + 8w)(7 + 5w) = (4w + -3)(10w + -7) Multiply (5 + 8w) * (7 + 5w) (5(7 + 5w) + 8w * (7 + 5w)) = (4w + -3)(10w + -7) ((7 * 5 + 5w * 5) + 8w * (7 + 5w)) = (4w + -3)(10w + -7) ((35 + 25w) + 8w * (7 + 5w)) = (4w + -3)(10w + -7) (35 + 25w + (7 * 8w + 5w * 8w)) = (4w + -3)(10w + -7) (35 + 25w + (56w + 40w2)) = (4w + -3)(10w + -7) Combine like terms: 25w + 56w = 81w (35 + 81w + 40w2) = (4w + -3)(10w + -7) Reorder the terms: 35 + 81w + 40w2 = (-3 + 4w)(10w + -7) Reorder the terms: 35 + 81w + 40w2 = (-3 + 4w)(-7 + 10w) Multiply (-3 + 4w) * (-7 + 10w) 35 + 81w + 40w2 = (-3(-7 + 10w) + 4w * (-7 + 10w)) 35 + 81w + 40w2 = ((-7 * -3 + 10w * -3) + 4w * (-7 + 10w)) 35 + 81w + 40w2 = ((21 + -30w) + 4w * (-7 + 10w)) 35 + 81w + 40w2 = (21 + -30w + (-7 * 4w + 10w * 4w)) 35 + 81w + 40w2 = (21 + -30w + (-28w + 40w2)) Combine like terms: -30w + -28w = -58w 35 + 81w + 40w2 = (21 + -58w + 40w2) Add '-40w2' to each side of the equation. 35 + 81w + 40w2 + -40w2 = 21 + -58w + 40w2 + -40w2 Combine like terms: 40w2 + -40w2 = 0 35 + 81w + 0 = 21 + -58w + 40w2 + -40w2 35 + 81w = 21 + -58w + 40w2 + -40w2 Combine like terms: 40w2 + -40w2 = 0 35 + 81w = 21 + -58w + 0 35 + 81w = 21 + -58w Solving 35 + 81w = 21 + -58w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '58w' to each side of the equation. 35 + 81w + 58w = 21 + -58w + 58w Combine like terms: 81w + 58w = 139w 35 + 139w = 21 + -58w + 58w Combine like terms: -58w + 58w = 0 35 + 139w = 21 + 0 35 + 139w = 21 Add '-35' to each side of the equation. 35 + -35 + 139w = 21 + -35 Combine like terms: 35 + -35 = 0 0 + 139w = 21 + -35 139w = 21 + -35 Combine like terms: 21 + -35 = -14 139w = -14 Divide each side by '139'. w = -0.1007194245 Simplifying w = -0.1007194245
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