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Simplifying (3a + 2)(2a + -7) = 0 Reorder the terms: (2 + 3a)(2a + -7) = 0 Reorder the terms: (2 + 3a)(-7 + 2a) = 0 Multiply (2 + 3a) * (-7 + 2a) (2(-7 + 2a) + 3a * (-7 + 2a)) = 0 ((-7 * 2 + 2a * 2) + 3a * (-7 + 2a)) = 0 ((-14 + 4a) + 3a * (-7 + 2a)) = 0 (-14 + 4a + (-7 * 3a + 2a * 3a)) = 0 (-14 + 4a + (-21a + 6a2)) = 0 Combine like terms: 4a + -21a = -17a (-14 + -17a + 6a2) = 0 Solving -14 + -17a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -3a)(7 + -2a) = 0Subproblem 1
Set the factor '(-2 + -3a)' equal to zero and attempt to solve: Simplifying -2 + -3a = 0 Solving -2 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3a = 0 + 2 -3a = 0 + 2 Combine like terms: 0 + 2 = 2 -3a = 2 Divide each side by '-3'. a = -0.6666666667 Simplifying a = -0.6666666667Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve: Simplifying 7 + -2a = 0 Solving 7 + -2a = 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 + -2a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2a = 0 + -7 -2a = 0 + -7 Combine like terms: 0 + -7 = -7 -2a = -7 Divide each side by '-2'. a = 3.5 Simplifying a = 3.5Solution
a = {-0.6666666667, 3.5}
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