(3a-4)*(3-7a)-4(2-3a)*(1+a)=(8+9a)*(5-a)

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Solution for (3a-4)*(3-7a)-4(2-3a)*(1+a)=(8+9a)*(5-a) equation:


Simplifying
(3a + -4)(3 + -7a) + -4(2 + -3a)(1 + a) = (8 + 9a)(5 + -1a)

Reorder the terms:
(-4 + 3a)(3 + -7a) + -4(2 + -3a)(1 + a) = (8 + 9a)(5 + -1a)

Multiply (-4 + 3a) * (3 + -7a)
(-4(3 + -7a) + 3a * (3 + -7a)) + -4(2 + -3a)(1 + a) = (8 + 9a)(5 + -1a)
((3 * -4 + -7a * -4) + 3a * (3 + -7a)) + -4(2 + -3a)(1 + a) = (8 + 9a)(5 + -1a)
((-12 + 28a) + 3a * (3 + -7a)) + -4(2 + -3a)(1 + a) = (8 + 9a)(5 + -1a)
(-12 + 28a + (3 * 3a + -7a * 3a)) + -4(2 + -3a)(1 + a) = (8 + 9a)(5 + -1a)
(-12 + 28a + (9a + -21a2)) + -4(2 + -3a)(1 + a) = (8 + 9a)(5 + -1a)

Combine like terms: 28a + 9a = 37a
(-12 + 37a + -21a2) + -4(2 + -3a)(1 + a) = (8 + 9a)(5 + -1a)

Multiply (2 + -3a) * (1 + a)
-12 + 37a + -21a2 + -4(2(1 + a) + -3a * (1 + a)) = (8 + 9a)(5 + -1a)
-12 + 37a + -21a2 + -4((1 * 2 + a * 2) + -3a * (1 + a)) = (8 + 9a)(5 + -1a)
-12 + 37a + -21a2 + -4((2 + 2a) + -3a * (1 + a)) = (8 + 9a)(5 + -1a)
-12 + 37a + -21a2 + -4(2 + 2a + (1 * -3a + a * -3a)) = (8 + 9a)(5 + -1a)
-12 + 37a + -21a2 + -4(2 + 2a + (-3a + -3a2)) = (8 + 9a)(5 + -1a)

Combine like terms: 2a + -3a = -1a
-12 + 37a + -21a2 + -4(2 + -1a + -3a2) = (8 + 9a)(5 + -1a)
-12 + 37a + -21a2 + (2 * -4 + -1a * -4 + -3a2 * -4) = (8 + 9a)(5 + -1a)
-12 + 37a + -21a2 + (-8 + 4a + 12a2) = (8 + 9a)(5 + -1a)

Reorder the terms:
-12 + -8 + 37a + 4a + -21a2 + 12a2 = (8 + 9a)(5 + -1a)

Combine like terms: -12 + -8 = -20
-20 + 37a + 4a + -21a2 + 12a2 = (8 + 9a)(5 + -1a)

Combine like terms: 37a + 4a = 41a
-20 + 41a + -21a2 + 12a2 = (8 + 9a)(5 + -1a)

Combine like terms: -21a2 + 12a2 = -9a2
-20 + 41a + -9a2 = (8 + 9a)(5 + -1a)

Multiply (8 + 9a) * (5 + -1a)
-20 + 41a + -9a2 = (8(5 + -1a) + 9a * (5 + -1a))
-20 + 41a + -9a2 = ((5 * 8 + -1a * 8) + 9a * (5 + -1a))
-20 + 41a + -9a2 = ((40 + -8a) + 9a * (5 + -1a))
-20 + 41a + -9a2 = (40 + -8a + (5 * 9a + -1a * 9a))
-20 + 41a + -9a2 = (40 + -8a + (45a + -9a2))

Combine like terms: -8a + 45a = 37a
-20 + 41a + -9a2 = (40 + 37a + -9a2)

Add '9a2' to each side of the equation.
-20 + 41a + -9a2 + 9a2 = 40 + 37a + -9a2 + 9a2

Combine like terms: -9a2 + 9a2 = 0
-20 + 41a + 0 = 40 + 37a + -9a2 + 9a2
-20 + 41a = 40 + 37a + -9a2 + 9a2

Combine like terms: -9a2 + 9a2 = 0
-20 + 41a = 40 + 37a + 0
-20 + 41a = 40 + 37a

Solving
-20 + 41a = 40 + 37a

Solving for variable 'a'.

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

Add '-37a' to each side of the equation.
-20 + 41a + -37a = 40 + 37a + -37a

Combine like terms: 41a + -37a = 4a
-20 + 4a = 40 + 37a + -37a

Combine like terms: 37a + -37a = 0
-20 + 4a = 40 + 0
-20 + 4a = 40

Add '20' to each side of the equation.
-20 + 20 + 4a = 40 + 20

Combine like terms: -20 + 20 = 0
0 + 4a = 40 + 20
4a = 40 + 20

Combine like terms: 40 + 20 = 60
4a = 60

Divide each side by '4'.
a = 15

Simplifying
a = 15

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