6(5a+1)-3(2a-8)=7(a+9)+3(5a-6)

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Solution for 6(5a+1)-3(2a-8)=7(a+9)+3(5a-6) equation: 


Simplifying
6(5a + 1) + -3(2a + -8) = 7(a + 9) + 3(5a + -6)

Reorder the terms:
6(1 + 5a) + -3(2a + -8) = 7(a + 9) + 3(5a + -6)
(1 * 6 + 5a * 6) + -3(2a + -8) = 7(a + 9) + 3(5a + -6)
(6 + 30a) + -3(2a + -8) = 7(a + 9) + 3(5a + -6)

Reorder the terms:
6 + 30a + -3(-8 + 2a) = 7(a + 9) + 3(5a + -6)
6 + 30a + (-8 * -3 + 2a * -3) = 7(a + 9) + 3(5a + -6)
6 + 30a + (24 + -6a) = 7(a + 9) + 3(5a + -6)

Reorder the terms:
6 + 24 + 30a + -6a = 7(a + 9) + 3(5a + -6)

Combine like terms: 6 + 24 = 30
30 + 30a + -6a = 7(a + 9) + 3(5a + -6)

Combine like terms: 30a + -6a = 24a
30 + 24a = 7(a + 9) + 3(5a + -6)

Reorder the terms:
30 + 24a = 7(9 + a) + 3(5a + -6)
30 + 24a = (9 * 7 + a * 7) + 3(5a + -6)
30 + 24a = (63 + 7a) + 3(5a + -6)

Reorder the terms:
30 + 24a = 63 + 7a + 3(-6 + 5a)
30 + 24a = 63 + 7a + (-6 * 3 + 5a * 3)
30 + 24a = 63 + 7a + (-18 + 15a)

Reorder the terms:
30 + 24a = 63 + -18 + 7a + 15a

Combine like terms: 63 + -18 = 45
30 + 24a = 45 + 7a + 15a

Combine like terms: 7a + 15a = 22a
30 + 24a = 45 + 22a

Solving
30 + 24a = 45 + 22a

Solving for variable 'a'.

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

Add '-22a' to each side of the equation.
30 + 24a + -22a = 45 + 22a + -22a

Combine like terms: 24a + -22a = 2a
30 + 2a = 45 + 22a + -22a

Combine like terms: 22a + -22a = 0
30 + 2a = 45 + 0
30 + 2a = 45

Add '-30' to each side of the equation.
30 + -30 + 2a = 45 + -30

Combine like terms: 30 + -30 = 0
0 + 2a = 45 + -30
2a = 45 + -30

Combine like terms: 45 + -30 = 15
2a = 15

Divide each side by '2'.
a = 7.5

Simplifying
a = 7.5

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