3a^2+23a+16=-8+6a

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Solution for 3a^2+23a+16=-8+6a equation: 


Simplifying
3a2 + 23a + 16 = -8 + 6a

Reorder the terms:
16 + 23a + 3a2 = -8 + 6a

Solving
16 + 23a + 3a2 = -8 + 6a

Solving for variable 'a'.

Reorder the terms:
16 + 8 + 23a + -6a + 3a2 = -8 + 6a + 8 + -6a

Combine like terms: 16 + 8 = 24
24 + 23a + -6a + 3a2 = -8 + 6a + 8 + -6a

Combine like terms: 23a + -6a = 17a
24 + 17a + 3a2 = -8 + 6a + 8 + -6a

Reorder the terms:
24 + 17a + 3a2 = -8 + 8 + 6a + -6a

Combine like terms: -8 + 8 = 0
24 + 17a + 3a2 = 0 + 6a + -6a
24 + 17a + 3a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
24 + 17a + 3a2 = 0

Factor a trinomial.
(3 + a)(8 + 3a) = 0


Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

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

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

Simplifying
a = -3

Subproblem 2
Set the factor '(8 + 3a)' equal to zero and attempt to solve:

Simplifying
8 + 3a = 0

Solving
8 + 3a = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3a = 0 + -8

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

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

Divide each side by '3'.
a = -2.666666667

Simplifying
a = -2.666666667
Solution
a = {-3, -2.666666667}

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