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Simplifying (4a + -3)(a + 4) = 0 Reorder the terms: (-3 + 4a)(a + 4) = 0 Reorder the terms: (-3 + 4a)(4 + a) = 0 Multiply (-3 + 4a) * (4 + a) (-3(4 + a) + 4a * (4 + a)) = 0 ((4 * -3 + a * -3) + 4a * (4 + a)) = 0 ((-12 + -3a) + 4a * (4 + a)) = 0 (-12 + -3a + (4 * 4a + a * 4a)) = 0 (-12 + -3a + (16a + 4a2)) = 0 Combine like terms: -3a + 16a = 13a (-12 + 13a + 4a2) = 0 Solving -12 + 13a + 4a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -1a)(3 + -4a) = 0Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 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 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 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 = {-4, 0.75}
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