Step-by-step explanation:
[tex] {a}^{2} + 7a + 12 = a + 4 \\ {a}^{2} + 7a - a - 4 + 12 = 0 \\ {a}^{2} + 6a + 8 = 0 \\ {a}^{2} + 4a + 2a + 8 = 0 \\ a(a + 4) + 2(a + 4) = 0 \\ (a + 4)(a + 2) = 0 \\ a + 4 = 0 \: or \: a + 2 = 0 \\ a = - 4 \: or \: a = - 2[/tex]
Answer:
a = -4 or a = -2
a² + 7a + 12 = a + 4
=> a² + 7a - a + 12 - 4 = 0
=> a² + 6a + 8 = 0
=> a² + 2a + 4a + 8 = 0
=> a(a + 2) + 4(a + 2) = 0
=> (a + 4)(a + 2) = 0
=> a = -4 or a = -2
