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Simplifying (3a + 7)(7a + -4) = 0 Reorder the terms: (7 + 3a)(7a + -4) = 0 Reorder the terms: (7 + 3a)(-4 + 7a) = 0 Multiply (7 + 3a) * (-4 + 7a) (7(-4 + 7a) + 3a * (-4 + 7a)) = 0 ((-4 * 7 + 7a * 7) + 3a * (-4 + 7a)) = 0 ((-28 + 49a) + 3a * (-4 + 7a)) = 0 (-28 + 49a + (-4 * 3a + 7a * 3a)) = 0 (-28 + 49a + (-12a + 21a2)) = 0 Combine like terms: 49a + -12a = 37a (-28 + 37a + 21a2) = 0 Solving -28 + 37a + 21a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -3a)(4 + -7a) = 0Subproblem 1
Set the factor '(-7 + -3a)' equal to zero and attempt to solve: Simplifying -7 + -3a = 0 Solving -7 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3a = 0 + 7 -3a = 0 + 7 Combine like terms: 0 + 7 = 7 -3a = 7 Divide each side by '-3'. a = -2.333333333 Simplifying a = -2.333333333Subproblem 2
Set the factor '(4 + -7a)' equal to zero and attempt to solve: Simplifying 4 + -7a = 0 Solving 4 + -7a = 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 + -7a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7a = 0 + -4 -7a = 0 + -4 Combine like terms: 0 + -4 = -4 -7a = -4 Divide each side by '-7'. a = 0.5714285714 Simplifying a = 0.5714285714Solution
a = {-2.333333333, 0.5714285714}
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