3(2a^2-1)-5a(a-3)+6a(3a-4)=85+19a^2+8a

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Solution for 3(2a^2-1)-5a(a-3)+6a(3a-4)=85+19a^2+8a equation: 


Simplifying
3(2a2 + -1) + -5a(a + -3) + 6a(3a + -4) = 85 + 19a2 + 8a

Reorder the terms:
3(-1 + 2a2) + -5a(a + -3) + 6a(3a + -4) = 85 + 19a2 + 8a
(-1 * 3 + 2a2 * 3) + -5a(a + -3) + 6a(3a + -4) = 85 + 19a2 + 8a
(-3 + 6a2) + -5a(a + -3) + 6a(3a + -4) = 85 + 19a2 + 8a

Reorder the terms:
-3 + 6a2 + -5a(-3 + a) + 6a(3a + -4) = 85 + 19a2 + 8a
-3 + 6a2 + (-3 * -5a + a * -5a) + 6a(3a + -4) = 85 + 19a2 + 8a
-3 + 6a2 + (15a + -5a2) + 6a(3a + -4) = 85 + 19a2 + 8a

Reorder the terms:
-3 + 6a2 + 15a + -5a2 + 6a(-4 + 3a) = 85 + 19a2 + 8a
-3 + 6a2 + 15a + -5a2 + (-4 * 6a + 3a * 6a) = 85 + 19a2 + 8a
-3 + 6a2 + 15a + -5a2 + (-24a + 18a2) = 85 + 19a2 + 8a

Reorder the terms:
-3 + 15a + -24a + 6a2 + -5a2 + 18a2 = 85 + 19a2 + 8a

Combine like terms: 15a + -24a = -9a
-3 + -9a + 6a2 + -5a2 + 18a2 = 85 + 19a2 + 8a

Combine like terms: 6a2 + -5a2 = 1a2
-3 + -9a + 1a2 + 18a2 = 85 + 19a2 + 8a

Combine like terms: 1a2 + 18a2 = 19a2
-3 + -9a + 19a2 = 85 + 19a2 + 8a

Reorder the terms:
-3 + -9a + 19a2 = 85 + 8a + 19a2

Add '-19a2' to each side of the equation.
-3 + -9a + 19a2 + -19a2 = 85 + 8a + 19a2 + -19a2

Combine like terms: 19a2 + -19a2 = 0
-3 + -9a + 0 = 85 + 8a + 19a2 + -19a2
-3 + -9a = 85 + 8a + 19a2 + -19a2

Combine like terms: 19a2 + -19a2 = 0
-3 + -9a = 85 + 8a + 0
-3 + -9a = 85 + 8a

Solving
-3 + -9a = 85 + 8a

Solving for variable 'a'.

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

Add '-8a' to each side of the equation.
-3 + -9a + -8a = 85 + 8a + -8a

Combine like terms: -9a + -8a = -17a
-3 + -17a = 85 + 8a + -8a

Combine like terms: 8a + -8a = 0
-3 + -17a = 85 + 0
-3 + -17a = 85

Add '3' to each side of the equation.
-3 + 3 + -17a = 85 + 3

Combine like terms: -3 + 3 = 0
0 + -17a = 85 + 3
-17a = 85 + 3

Combine like terms: 85 + 3 = 88
-17a = 88

Divide each side by '-17'.
a = -5.176470588

Simplifying
a = -5.176470588

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