(a+2a+5)(a-3a-7)=0

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Solution for (a+2a+5)(a-3a-7)=0 equation: 


Simplifying
(a + 2a + 5)(a + -3a + -7) = 0

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

Combine like terms: a + 2a = 3a
(5 + 3a)(a + -3a + -7) = 0

Reorder the terms:
(5 + 3a)(-7 + a + -3a) = 0

Combine like terms: a + -3a = -2a
(5 + 3a)(-7 + -2a) = 0

Multiply (5 + 3a) * (-7 + -2a)
(5(-7 + -2a) + 3a * (-7 + -2a)) = 0
((-7 * 5 + -2a * 5) + 3a * (-7 + -2a)) = 0
((-35 + -10a) + 3a * (-7 + -2a)) = 0
(-35 + -10a + (-7 * 3a + -2a * 3a)) = 0
(-35 + -10a + (-21a + -6a2)) = 0

Combine like terms: -10a + -21a = -31a
(-35 + -31a + -6a2) = 0

Solving
-35 + -31a + -6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 31a + 6a2) = 0

Factor a trinomial.
-1((7 + 2a)(5 + 3a)) = 0

Ignore the factor -1.

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 '(5 + 3a)' equal to zero and attempt to solve:

Simplifying
5 + 3a = 0

Solving
5 + 3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3a = 0 + -5
3a = 0 + -5

Combine like terms: 0 + -5 = -5
3a = -5

Divide each side by '3'.
a = -1.666666667

Simplifying
a = -1.666666667
Solution
a = {-3.5, -1.666666667}

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