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Simplifying (10r + 8) * and(5r + -12) = 0 Reorder the terms: (8 + 10r) * and(5r + -12) = 0 Reorder the terms: (8 + 10r) * adn(-12 + 5r) = 0 Reorder the terms for easier multiplication: adn(8 + 10r)(-12 + 5r) = 0 Multiply (8 + 10r) * (-12 + 5r) adn(8(-12 + 5r) + 10r * (-12 + 5r)) = 0 adn((-12 * 8 + 5r * 8) + 10r * (-12 + 5r)) = 0 adn((-96 + 40r) + 10r * (-12 + 5r)) = 0 adn(-96 + 40r + (-12 * 10r + 5r * 10r)) = 0 adn(-96 + 40r + (-120r + 50r2)) = 0 Combine like terms: 40r + -120r = -80r adn(-96 + -80r + 50r2) = 0 (-96 * adn + -80r * adn + 50r2 * adn) = 0 (-96adn + -80adnr + 50adnr2) = 0 Solving -96adn + -80adnr + 50adnr2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2adn'. 2adn(-48 + -40r + 25r2) = 0 Factor a trinomial. 2adn((-4 + -5r)(12 + -5r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'adn' equal to zero and attempt to solve: Simplifying adn = 0 Solving adn = 0 Move all terms containing a to the left, all other terms to the right. Simplifying adn = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-4 + -5r)' equal to zero and attempt to solve: Simplifying -4 + -5r = 0 Solving -4 + -5r = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5r = 0 + 4 -5r = 0 + 4 Combine like terms: 0 + 4 = 4 -5r = 4 Add '5r' to each side of the equation. -5r + 5r = 4 + 5r Combine like terms: -5r + 5r = 0 0 = 4 + 5r Simplifying 0 = 4 + 5r The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(12 + -5r)' equal to zero and attempt to solve: Simplifying 12 + -5r = 0 Solving 12 + -5r = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -5r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5r = 0 + -12 -5r = 0 + -12 Combine like terms: 0 + -12 = -12 -5r = -12 Add '5r' to each side of the equation. -5r + 5r = -12 + 5r Combine like terms: -5r + 5r = 0 0 = -12 + 5r Simplifying 0 = -12 + 5r The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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