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Simplifying (4a + -3)(2a + 7) = 0 Reorder the terms: (-3 + 4a)(2a + 7) = 0 Reorder the terms: (-3 + 4a)(7 + 2a) = 0 Multiply (-3 + 4a) * (7 + 2a) (-3(7 + 2a) + 4a * (7 + 2a)) = 0 ((7 * -3 + 2a * -3) + 4a * (7 + 2a)) = 0 ((-21 + -6a) + 4a * (7 + 2a)) = 0 (-21 + -6a + (7 * 4a + 2a * 4a)) = 0 (-21 + -6a + (28a + 8a2)) = 0 Combine like terms: -6a + 28a = 22a (-21 + 22a + 8a2) = 0 Solving -21 + 22a + 8a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -2a)(3 + -4a) = 0Subproblem 1
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 = -3.5Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve: Simplifying 3 + -4a = 0 Solving 3 + -4a = 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 + -4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4a = 0 + -3 -4a = 0 + -3 Combine like terms: 0 + -3 = -3 -4a = -3 Divide each side by '-4'. a = 0.75 Simplifying a = 0.75Solution
a = {-3.5, 0.75}
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