a(3+2a)+4(2+2a)-5a=

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Solution for a(3+2a)+4(2+2a)-5a= equation: 


Simplifying
a(3 + 2a) + 4(2 + 2a) + -5a = 0
(3 * a + 2a * a) + 4(2 + 2a) + -5a = 0
(3a + 2a2) + 4(2 + 2a) + -5a = 0
3a + 2a2 + (2 * 4 + 2a * 4) + -5a = 0
3a + 2a2 + (8 + 8a) + -5a = 0

Reorder the terms:
8 + 3a + 8a + -5a + 2a2 = 0

Combine like terms: 3a + 8a = 11a
8 + 11a + -5a + 2a2 = 0

Combine like terms: 11a + -5a = 6a
8 + 6a + 2a2 = 0

Solving
8 + 6a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 3a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 3a + a2)' equal to zero and attempt to solve:

Simplifying
4 + 3a + a2 = 0

Solving
4 + 3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 3a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + 3a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3a + a2 = 0 + -4
3a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
3a + a2 = -4

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = -4 + 2.25

Reorder the terms:
2.25 + 3a + a2 = -4 + 2.25

Combine like terms: -4 + 2.25 = -1.75
2.25 + 3a + a2 = -1.75

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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