(2a+7)(a+3)=0

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Solution for (2a+7)(a+3)=0 equation:


Simplifying
(2a + 7)(a + 3) = 0

Reorder the terms:
(7 + 2a)(a + 3) = 0

Reorder the terms:
(7 + 2a)(3 + a) = 0

Multiply (7 + 2a) * (3 + a)
(7(3 + a) + 2a * (3 + a)) = 0
((3 * 7 + a * 7) + 2a * (3 + a)) = 0
((21 + 7a) + 2a * (3 + a)) = 0
(21 + 7a + (3 * 2a + a * 2a)) = 0
(21 + 7a + (6a + 2a2)) = 0

Combine like terms: 7a + 6a = 13a
(21 + 13a + 2a2) = 0

Solving
21 + 13a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7 + 2a)(3 + a) = 0

Subproblem 1

Set the factor '(7 + 2a)' equal to zero and attempt to solve: Simplifying 7 + 2a = 0 Solving 7 + 2a = 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 + 2a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2a = 0 + -7 2a = 0 + -7 Combine like terms: 0 + -7 = -7 2a = -7 Divide each side by '2'. a = -3.5 Simplifying a = -3.5

Subproblem 2

Set the factor '(3 + a)' equal to zero and attempt to solve: Simplifying 3 + a = 0 Solving 3 + a = 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 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3

Solution

a = {-3.5, -3}

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