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Simplifying 3a(a + -4) + 7(a + -4) = 0 Reorder the terms: 3a(-4 + a) + 7(a + -4) = 0 (-4 * 3a + a * 3a) + 7(a + -4) = 0 (-12a + 3a2) + 7(a + -4) = 0 Reorder the terms: -12a + 3a2 + 7(-4 + a) = 0 -12a + 3a2 + (-4 * 7 + a * 7) = 0 -12a + 3a2 + (-28 + 7a) = 0 Reorder the terms: -28 + -12a + 7a + 3a2 = 0 Combine like terms: -12a + 7a = -5a -28 + -5a + 3a2 = 0 Solving -28 + -5a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -3a)(4 + -1a) = 0Subproblem 1
Set the factor '(-7 + -3a)' equal to zero and attempt to solve: Simplifying -7 + -3a = 0 Solving -7 + -3a = 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 + -3a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3a = 0 + 7 -3a = 0 + 7 Combine like terms: 0 + 7 = 7 -3a = 7 Divide each side by '-3'. a = -2.333333333 Simplifying a = -2.333333333Subproblem 2
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 = 4Solution
a = {-2.333333333, 4}
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