(3-2a)(1+3a)=(5-a)(6a+7)

Solution for (3-2a)(1+3a)=(5-a)(6a+7) equation:

Simplifying
(3 + -2a)(1 + 3a) = (5 + -1a)(6a + 7)

Multiply (3 + -2a) * (1 + 3a)
(3(1 + 3a) + -2a * (1 + 3a)) = (5 + -1a)(6a + 7)
((1 * 3 + 3a * 3) + -2a * (1 + 3a)) = (5 + -1a)(6a + 7)
((3 + 9a) + -2a * (1 + 3a)) = (5 + -1a)(6a + 7)
(3 + 9a + (1 * -2a + 3a * -2a)) = (5 + -1a)(6a + 7)
(3 + 9a + (-2a + -6a2)) = (5 + -1a)(6a + 7)

Combine like terms: 9a + -2a = 7a
(3 + 7a + -6a2) = (5 + -1a)(6a + 7)

Reorder the terms:
3 + 7a + -6a2 = (5 + -1a)(7 + 6a)

Multiply (5 + -1a) * (7 + 6a)
3 + 7a + -6a2 = (5(7 + 6a) + -1a * (7 + 6a))
3 + 7a + -6a2 = ((7 * 5 + 6a * 5) + -1a * (7 + 6a))
3 + 7a + -6a2 = ((35 + 30a) + -1a * (7 + 6a))
3 + 7a + -6a2 = (35 + 30a + (7 * -1a + 6a * -1a))
3 + 7a + -6a2 = (35 + 30a + (-7a + -6a2))

Combine like terms: 30a + -7a = 23a
3 + 7a + -6a2 = (35 + 23a + -6a2)

Add '6a2' to each side of the equation.
3 + 7a + -6a2 + 6a2 = 35 + 23a + -6a2 + 6a2

Combine like terms: -6a2 + 6a2 = 0
3 + 7a + 0 = 35 + 23a + -6a2 + 6a2
3 + 7a = 35 + 23a + -6a2 + 6a2

Combine like terms: -6a2 + 6a2 = 0
3 + 7a = 35 + 23a + 0
3 + 7a = 35 + 23a

Solving
3 + 7a = 35 + 23a

Solving for variable 'a'.

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

Add '-23a' to each side of the equation.
3 + 7a + -23a = 35 + 23a + -23a

Combine like terms: 7a + -23a = -16a
3 + -16a = 35 + 23a + -23a

Combine like terms: 23a + -23a = 0
3 + -16a = 35 + 0
3 + -16a = 35

Add '-3' to each side of the equation.
3 + -3 + -16a = 35 + -3

Combine like terms: 3 + -3 = 0
0 + -16a = 35 + -3
-16a = 35 + -3

Combine like terms: 35 + -3 = 32
-16a = 32

Divide each side by '-16'.
a = -2

Simplifying
a = -2