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Simplifying (3a + 1)(4a + -7) = 0 Reorder the terms: (1 + 3a)(4a + -7) = 0 Reorder the terms: (1 + 3a)(-7 + 4a) = 0 Multiply (1 + 3a) * (-7 + 4a) (1(-7 + 4a) + 3a * (-7 + 4a)) = 0 ((-7 * 1 + 4a * 1) + 3a * (-7 + 4a)) = 0 ((-7 + 4a) + 3a * (-7 + 4a)) = 0 (-7 + 4a + (-7 * 3a + 4a * 3a)) = 0 (-7 + 4a + (-21a + 12a2)) = 0 Combine like terms: 4a + -21a = -17a (-7 + -17a + 12a2) = 0 Solving -7 + -17a + 12a2 = 0 Solving for variable 'a'. Factor a trinomial. (-1 + -3a)(7 + -4a) = 0Subproblem 1
Set the factor '(-1 + -3a)' equal to zero and attempt to solve: Simplifying -1 + -3a = 0 Solving -1 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3a = 0 + 1 -3a = 0 + 1 Combine like terms: 0 + 1 = 1 -3a = 1 Divide each side by '-3'. a = -0.3333333333 Simplifying a = -0.3333333333Subproblem 2
Set the factor '(7 + -4a)' equal to zero and attempt to solve: Simplifying 7 + -4a = 0 Solving 7 + -4a = 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 + -4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a = 0 + -7 -4a = 0 + -7 Combine like terms: 0 + -7 = -7 -4a = -7 Divide each side by '-4'. a = 1.75 Simplifying a = 1.75Solution
a = {-0.3333333333, 1.75}
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