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Simplifying (10r + 7)(3r + -4) = 0 Reorder the terms: (7 + 10r)(3r + -4) = 0 Reorder the terms: (7 + 10r)(-4 + 3r) = 0 Multiply (7 + 10r) * (-4 + 3r) (7(-4 + 3r) + 10r * (-4 + 3r)) = 0 ((-4 * 7 + 3r * 7) + 10r * (-4 + 3r)) = 0 ((-28 + 21r) + 10r * (-4 + 3r)) = 0 (-28 + 21r + (-4 * 10r + 3r * 10r)) = 0 (-28 + 21r + (-40r + 30r2)) = 0 Combine like terms: 21r + -40r = -19r (-28 + -19r + 30r2) = 0 Solving -28 + -19r + 30r2 = 0 Solving for variable 'r'. Factor a trinomial. (-7 + -10r)(4 + -3r) = 0Subproblem 1
Set the factor '(-7 + -10r)' equal to zero and attempt to solve: Simplifying -7 + -10r = 0 Solving -7 + -10r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -10r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10r = 0 + 7 -10r = 0 + 7 Combine like terms: 0 + 7 = 7 -10r = 7 Divide each side by '-10'. r = -0.7 Simplifying r = -0.7Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve: Simplifying 4 + -3r = 0 Solving 4 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3r = 0 + -4 -3r = 0 + -4 Combine like terms: 0 + -4 = -4 -3r = -4 Divide each side by '-3'. r = 1.333333333 Simplifying r = 1.333333333Solution
r = {-0.7, 1.333333333}
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