(a+3)(a-3)=(a+6)(a-5)

Solution for (a+3)(a-3)=(a+6)(a-5) equation:

Simplifying
(a + 3)(a + -3) = (a + 6)(a + -5)

Reorder the terms:
(3 + a)(a + -3) = (a + 6)(a + -5)

Reorder the terms:
(3 + a)(-3 + a) = (a + 6)(a + -5)

Multiply (3 + a) * (-3 + a)
(3(-3 + a) + a(-3 + a)) = (a + 6)(a + -5)
((-3 * 3 + a * 3) + a(-3 + a)) = (a + 6)(a + -5)
((-9 + 3a) + a(-3 + a)) = (a + 6)(a + -5)
(-9 + 3a + (-3 * a + a * a)) = (a + 6)(a + -5)
(-9 + 3a + (-3a + a2)) = (a + 6)(a + -5)

Combine like terms: 3a + -3a = 0
(-9 + 0 + a2) = (a + 6)(a + -5)
(-9 + a2) = (a + 6)(a + -5)

Reorder the terms:
-9 + a2 = (6 + a)(a + -5)

Reorder the terms:
-9 + a2 = (6 + a)(-5 + a)

Multiply (6 + a) * (-5 + a)
-9 + a2 = (6(-5 + a) + a(-5 + a))
-9 + a2 = ((-5 * 6 + a * 6) + a(-5 + a))
-9 + a2 = ((-30 + 6a) + a(-5 + a))
-9 + a2 = (-30 + 6a + (-5 * a + a * a))
-9 + a2 = (-30 + 6a + (-5a + a2))

Combine like terms: 6a + -5a = 1a
-9 + a2 = (-30 + 1a + a2)

Add '-1a2' to each side of the equation.
-9 + a2 + -1a2 = -30 + 1a + a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-9 + 0 = -30 + 1a + a2 + -1a2
-9 = -30 + 1a + a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-9 = -30 + 1a + 0
-9 = -30 + 1a

Solving
-9 = -30 + 1a

Solving for variable 'a'.

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

Add '-1a' to each side of the equation.
-9 + -1a = -30 + 1a + -1a

Combine like terms: 1a + -1a = 0
-9 + -1a = -30 + 0
-9 + -1a = -30

Add '9' to each side of the equation.
-9 + 9 + -1a = -30 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = -30 + 9
-1a = -30 + 9

Combine like terms: -30 + 9 = -21
-1a = -21

Divide each side by '-1'.
a = 21

Simplifying
a = 21