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Simplifying 12(u + v) * 2 + 11(u + v) + -5 = 12(u + v) * 2 + 11(u + v) + -5 Reorder the terms for easier multiplication: 12 * 2(u + v) + 11(u + v) + -5 = 12(u + v) * 2 + 11(u + v) + -5 Multiply 12 * 2 24(u + v) + 11(u + v) + -5 = 12(u + v) * 2 + 11(u + v) + -5 (u * 24 + v * 24) + 11(u + v) + -5 = 12(u + v) * 2 + 11(u + v) + -5 (24u + 24v) + 11(u + v) + -5 = 12(u + v) * 2 + 11(u + v) + -5 24u + 24v + (u * 11 + v * 11) + -5 = 12(u + v) * 2 + 11(u + v) + -5 24u + 24v + (11u + 11v) + -5 = 12(u + v) * 2 + 11(u + v) + -5 Reorder the terms: -5 + 24u + 11u + 24v + 11v = 12(u + v) * 2 + 11(u + v) + -5 Combine like terms: 24u + 11u = 35u -5 + 35u + 24v + 11v = 12(u + v) * 2 + 11(u + v) + -5 Combine like terms: 24v + 11v = 35v -5 + 35u + 35v = 12(u + v) * 2 + 11(u + v) + -5 Reorder the terms for easier multiplication: -5 + 35u + 35v = 12 * 2(u + v) + 11(u + v) + -5 Multiply 12 * 2 -5 + 35u + 35v = 24(u + v) + 11(u + v) + -5 -5 + 35u + 35v = (u * 24 + v * 24) + 11(u + v) + -5 -5 + 35u + 35v = (24u + 24v) + 11(u + v) + -5 -5 + 35u + 35v = 24u + 24v + (u * 11 + v * 11) + -5 -5 + 35u + 35v = 24u + 24v + (11u + 11v) + -5 Reorder the terms: -5 + 35u + 35v = -5 + 24u + 11u + 24v + 11v Combine like terms: 24u + 11u = 35u -5 + 35u + 35v = -5 + 35u + 24v + 11v Combine like terms: 24v + 11v = 35v -5 + 35u + 35v = -5 + 35u + 35v Add '5' to each side of the equation. -5 + 35u + 5 + 35v = -5 + 35u + 5 + 35v Reorder the terms: -5 + 5 + 35u + 35v = -5 + 35u + 5 + 35v Combine like terms: -5 + 5 = 0 0 + 35u + 35v = -5 + 35u + 5 + 35v 35u + 35v = -5 + 35u + 5 + 35v Reorder the terms: 35u + 35v = -5 + 5 + 35u + 35v Combine like terms: -5 + 5 = 0 35u + 35v = 0 + 35u + 35v 35u + 35v = 35u + 35v Add '-35u' to each side of the equation. 35u + -35u + 35v = 35u + -35u + 35v Combine like terms: 35u + -35u = 0 0 + 35v = 35u + -35u + 35v 35v = 35u + -35u + 35v Combine like terms: 35u + -35u = 0 35v = 0 + 35v 35v = 35v Add '-35v' to each side of the equation. 35v + -35v = 35v + -35v Combine like terms: 35v + -35v = 0 0 = 35v + -35v Combine like terms: 35v + -35v = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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