a(5+3a)=2a-7

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Solution for a(5+3a)=2a-7 equation: 


Simplifying
a(5 + 3a) = 2a + -7
(5 * a + 3a * a) = 2a + -7
(5a + 3a2) = 2a + -7

Reorder the terms:
5a + 3a2 = -7 + 2a

Solving
5a + 3a2 = -7 + 2a

Solving for variable 'a'.

Reorder the terms:
7 + 5a + -2a + 3a2 = -7 + 2a + 7 + -2a

Combine like terms: 5a + -2a = 3a
7 + 3a + 3a2 = -7 + 2a + 7 + -2a

Reorder the terms:
7 + 3a + 3a2 = -7 + 7 + 2a + -2a

Combine like terms: -7 + 7 = 0
7 + 3a + 3a2 = 0 + 2a + -2a
7 + 3a + 3a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
7 + 3a + 3a2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2.333333333 + a + a2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + a + -2.333333333 + a2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + a + a2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + a + a2 = 0 + -2.333333333
a + a2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
a + a2 = -2.333333333

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + a2 = -2.333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + a2 = -2.333333333 + 0.25

Combine like terms: -2.333333333 + 0.25 = -2.083333333
1.25 + a2 = -2.083333333

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -2.083333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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