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Simplifying (a + 7)(2a + -3) = 0 Reorder the terms: (7 + a)(2a + -3) = 0 Reorder the terms: (7 + a)(-3 + 2a) = 0 Multiply (7 + a) * (-3 + 2a) (7(-3 + 2a) + a(-3 + 2a)) = 0 ((-3 * 7 + 2a * 7) + a(-3 + 2a)) = 0 ((-21 + 14a) + a(-3 + 2a)) = 0 (-21 + 14a + (-3 * a + 2a * a)) = 0 (-21 + 14a + (-3a + 2a2)) = 0 Combine like terms: 14a + -3a = 11a (-21 + 11a + 2a2) = 0 Solving -21 + 11a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -1a)(3 + -2a) = 0Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve: Simplifying -7 + -1a = 0 Solving -7 + -1a = 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 + -1a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1a = 0 + 7 -1a = 0 + 7 Combine like terms: 0 + 7 = 7 -1a = 7 Divide each side by '-1'. a = -7 Simplifying a = -7Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {-7, 1.5}
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