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Simplifying -4(a + -7) = a(a + -1) Reorder the terms: -4(-7 + a) = a(a + -1) (-7 * -4 + a * -4) = a(a + -1) (28 + -4a) = a(a + -1) Reorder the terms: 28 + -4a = a(-1 + a) 28 + -4a = (-1 * a + a * a) 28 + -4a = (-1a + a2) Solving 28 + -4a = -1a + a2 Solving for variable 'a'. Combine like terms: -4a + a = -3a 28 + -3a + -1a2 = -1a + a2 + a + -1a2 Reorder the terms: 28 + -3a + -1a2 = -1a + a + a2 + -1a2 Combine like terms: -1a + a = 0 28 + -3a + -1a2 = 0 + a2 + -1a2 28 + -3a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 28 + -3a + -1a2 = 0 Factor a trinomial. (4 + -1a)(7 + a) = 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 '(7 + a)' equal to zero and attempt to solve: Simplifying 7 + a = 0 Solving 7 + a = 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 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7Solution
a = {4, -7}
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