9[7(3a+2b-4)+12(a-2)]+3(5a-8b)=0

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Solution for 9[7(3a+2b-4)+12(a-2)]+3(5a-8b)=0 equation: 


Simplifying
9[7(3a + 2b + -4) + 12(a + -2)] + 3(5a + -8b) = 0

Reorder the terms:
9[7(-4 + 3a + 2b) + 12(a + -2)] + 3(5a + -8b) = 0
9[(-4 * 7 + 3a * 7 + 2b * 7) + 12(a + -2)] + 3(5a + -8b) = 0
9[(-28 + 21a + 14b) + 12(a + -2)] + 3(5a + -8b) = 0

Reorder the terms:
9[-28 + 21a + 14b + 12(-2 + a)] + 3(5a + -8b) = 0
9[-28 + 21a + 14b + (-2 * 12 + a * 12)] + 3(5a + -8b) = 0
9[-28 + 21a + 14b + (-24 + 12a)] + 3(5a + -8b) = 0

Reorder the terms:
9[-28 + -24 + 21a + 12a + 14b] + 3(5a + -8b) = 0

Combine like terms: -28 + -24 = -52
9[-52 + 21a + 12a + 14b] + 3(5a + -8b) = 0

Combine like terms: 21a + 12a = 33a
9[-52 + 33a + 14b] + 3(5a + -8b) = 0
[-52 * 9 + 33a * 9 + 14b * 9] + 3(5a + -8b) = 0
[-468 + 297a + 126b] + 3(5a + -8b) = 0
-468 + 297a + 126b + (5a * 3 + -8b * 3) = 0
-468 + 297a + 126b + (15a + -24b) = 0

Reorder the terms:
-468 + 297a + 15a + 126b + -24b = 0

Combine like terms: 297a + 15a = 312a
-468 + 312a + 126b + -24b = 0

Combine like terms: 126b + -24b = 102b
-468 + 312a + 102b = 0

Solving
-468 + 312a + 102b = 0

Solving for variable 'a'.

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

Add '468' to each side of the equation.
-468 + 312a + 468 + 102b = 0 + 468

Reorder the terms:
-468 + 468 + 312a + 102b = 0 + 468

Combine like terms: -468 + 468 = 0
0 + 312a + 102b = 0 + 468
312a + 102b = 0 + 468

Combine like terms: 0 + 468 = 468
312a + 102b = 468

Add '-102b' to each side of the equation.
312a + 102b + -102b = 468 + -102b

Combine like terms: 102b + -102b = 0
312a + 0 = 468 + -102b
312a = 468 + -102b

Divide each side by '312'.
a = 1.5 + -0.3269230769b

Simplifying
a = 1.5 + -0.3269230769b

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