(2a-3)(a+1)=(a+3)(a+9)

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Solution for (2a-3)(a+1)=(a+3)(a+9) equation: 


Simplifying
(2a + -3)(a + 1) = (a + 3)(a + 9)

Reorder the terms:
(-3 + 2a)(a + 1) = (a + 3)(a + 9)

Reorder the terms:
(-3 + 2a)(1 + a) = (a + 3)(a + 9)

Multiply (-3 + 2a) * (1 + a)
(-3(1 + a) + 2a * (1 + a)) = (a + 3)(a + 9)
((1 * -3 + a * -3) + 2a * (1 + a)) = (a + 3)(a + 9)
((-3 + -3a) + 2a * (1 + a)) = (a + 3)(a + 9)
(-3 + -3a + (1 * 2a + a * 2a)) = (a + 3)(a + 9)
(-3 + -3a + (2a + 2a2)) = (a + 3)(a + 9)

Combine like terms: -3a + 2a = -1a
(-3 + -1a + 2a2) = (a + 3)(a + 9)

Reorder the terms:
-3 + -1a + 2a2 = (3 + a)(a + 9)

Reorder the terms:
-3 + -1a + 2a2 = (3 + a)(9 + a)

Multiply (3 + a) * (9 + a)
-3 + -1a + 2a2 = (3(9 + a) + a(9 + a))
-3 + -1a + 2a2 = ((9 * 3 + a * 3) + a(9 + a))
-3 + -1a + 2a2 = ((27 + 3a) + a(9 + a))
-3 + -1a + 2a2 = (27 + 3a + (9 * a + a * a))
-3 + -1a + 2a2 = (27 + 3a + (9a + a2))

Combine like terms: 3a + 9a = 12a
-3 + -1a + 2a2 = (27 + 12a + a2)

Solving
-3 + -1a + 2a2 = 27 + 12a + a2

Solving for variable 'a'.

Reorder the terms:
-3 + -27 + -1a + -12a + 2a2 + -1a2 = 27 + 12a + a2 + -27 + -12a + -1a2

Combine like terms: -3 + -27 = -30
-30 + -1a + -12a + 2a2 + -1a2 = 27 + 12a + a2 + -27 + -12a + -1a2

Combine like terms: -1a + -12a = -13a
-30 + -13a + 2a2 + -1a2 = 27 + 12a + a2 + -27 + -12a + -1a2

Combine like terms: 2a2 + -1a2 = 1a2
-30 + -13a + 1a2 = 27 + 12a + a2 + -27 + -12a + -1a2

Reorder the terms:
-30 + -13a + 1a2 = 27 + -27 + 12a + -12a + a2 + -1a2

Combine like terms: 27 + -27 = 0
-30 + -13a + 1a2 = 0 + 12a + -12a + a2 + -1a2
-30 + -13a + 1a2 = 12a + -12a + a2 + -1a2

Combine like terms: 12a + -12a = 0
-30 + -13a + 1a2 = 0 + a2 + -1a2
-30 + -13a + 1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-30 + -13a + 1a2 = 0

Factor a trinomial.
(-2 + -1a)(15 + -1a) = 0


Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1a = 0 + 2
-1a = 0 + 2

Combine like terms: 0 + 2 = 2
-1a = 2

Divide each side by '-1'.
a = -2

Simplifying
a = -2

Subproblem 2
Set the factor '(15 + -1a)' equal to zero and attempt to solve:

Simplifying
15 + -1a = 0

Solving
15 + -1a = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1a = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1a = 0 + -15
-1a = 0 + -15

Combine like terms: 0 + -15 = -15
-1a = -15

Divide each side by '-1'.
a = 15

Simplifying
a = 15
Solution
a = {-2, 15}

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