=(a-4)(a+7)

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Solution for =(a-4)(a+7) equation:


Simplifying
0 = (a + -4)(a + 7)

Reorder the terms:
0 = (-4 + a)(a + 7)

Reorder the terms:
0 = (-4 + a)(7 + a)

Multiply (-4 + a) * (7 + a)
0 = (-4(7 + a) + a(7 + a))
0 = ((7 * -4 + a * -4) + a(7 + a))
0 = ((-28 + -4a) + a(7 + a))
0 = (-28 + -4a + (7 * a + a * a))
0 = (-28 + -4a + (7a + a2))

Combine like terms: -4a + 7a = 3a
0 = (-28 + 3a + a2)

Solving
0 = -28 + 3a + a2

Solving for variable 'a'.

Combine like terms: 0 + 28 = 28
28 + -3a + -1a2 = -28 + 3a + a2 + 28 + -3a + -1a2

Reorder the terms:
28 + -3a + -1a2 = -28 + 28 + 3a + -3a + a2 + -1a2

Combine like terms: -28 + 28 = 0
28 + -3a + -1a2 = 0 + 3a + -3a + a2 + -1a2
28 + -3a + -1a2 = 3a + -3a + a2 + -1a2

Combine like terms: 3a + -3a = 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) = 0

Subproblem 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 = 4

Subproblem 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 = -7

Solution

a = {4, -7}

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