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

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


Simplifying
a(2a + 3) + -2(3a + -5) = 0

Reorder the terms:
a(3 + 2a) + -2(3a + -5) = 0
(3 * a + 2a * a) + -2(3a + -5) = 0
(3a + 2a2) + -2(3a + -5) = 0

Reorder the terms:
3a + 2a2 + -2(-5 + 3a) = 0
3a + 2a2 + (-5 * -2 + 3a * -2) = 0
3a + 2a2 + (10 + -6a) = 0

Reorder the terms:
10 + 3a + -6a + 2a2 = 0

Combine like terms: 3a + -6a = -3a
10 + -3a + 2a2 = 0

Solving
10 + -3a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
5 + -1.5a + a2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -1.5a + -5 + a2 = 0 + -5

Reorder the terms:
5 + -5 + -1.5a + a2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1.5a + a2 = 0 + -5
-1.5a + a2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1.5a + a2 = -5

The a term is -1.5a.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5a + 0.5625 + a2 = -5 + 0.5625

Reorder the terms:
0.5625 + -1.5a + a2 = -5 + 0.5625

Combine like terms: -5 + 0.5625 = -4.4375
0.5625 + -1.5a + a2 = -4.4375

Factor a perfect square on the left side:
(a + -0.75)(a + -0.75) = -4.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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