(a+2)(3a-1)-a(5a+3)-(2a-3)(5a-2)=

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Solution for (a+2)(3a-1)-a(5a+3)-(2a-3)(5a-2)= equation: 


Simplifying
(a + 2)(3a + -1) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0

Reorder the terms:
(2 + a)(3a + -1) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0

Reorder the terms:
(2 + a)(-1 + 3a) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0

Multiply (2 + a) * (-1 + 3a)
(2(-1 + 3a) + a(-1 + 3a)) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0
((-1 * 2 + 3a * 2) + a(-1 + 3a)) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0
((-2 + 6a) + a(-1 + 3a)) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0
(-2 + 6a + (-1 * a + 3a * a)) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0
(-2 + 6a + (-1a + 3a2)) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0

Combine like terms: 6a + -1a = 5a
(-2 + 5a + 3a2) + -1a(5a + 3) + -1(2a + -3)(5a + -2) = 0

Reorder the terms:
-2 + 5a + 3a2 + -1a(3 + 5a) + -1(2a + -3)(5a + -2) = 0
-2 + 5a + 3a2 + (3 * -1a + 5a * -1a) + -1(2a + -3)(5a + -2) = 0
-2 + 5a + 3a2 + (-3a + -5a2) + -1(2a + -3)(5a + -2) = 0

Reorder the terms:
-2 + 5a + 3a2 + -3a + -5a2 + -1(-3 + 2a)(5a + -2) = 0

Reorder the terms:
-2 + 5a + 3a2 + -3a + -5a2 + -1(-3 + 2a)(-2 + 5a) = 0

Multiply (-3 + 2a) * (-2 + 5a)
-2 + 5a + 3a2 + -3a + -5a2 + -1(-3(-2 + 5a) + 2a * (-2 + 5a)) = 0
-2 + 5a + 3a2 + -3a + -5a2 + -1((-2 * -3 + 5a * -3) + 2a * (-2 + 5a)) = 0
-2 + 5a + 3a2 + -3a + -5a2 + -1((6 + -15a) + 2a * (-2 + 5a)) = 0
-2 + 5a + 3a2 + -3a + -5a2 + -1(6 + -15a + (-2 * 2a + 5a * 2a)) = 0
-2 + 5a + 3a2 + -3a + -5a2 + -1(6 + -15a + (-4a + 10a2)) = 0

Combine like terms: -15a + -4a = -19a
-2 + 5a + 3a2 + -3a + -5a2 + -1(6 + -19a + 10a2) = 0
-2 + 5a + 3a2 + -3a + -5a2 + (6 * -1 + -19a * -1 + 10a2 * -1) = 0
-2 + 5a + 3a2 + -3a + -5a2 + (-6 + 19a + -10a2) = 0

Reorder the terms:
-2 + -6 + 5a + -3a + 19a + 3a2 + -5a2 + -10a2 = 0

Combine like terms: -2 + -6 = -8
-8 + 5a + -3a + 19a + 3a2 + -5a2 + -10a2 = 0

Combine like terms: 5a + -3a = 2a
-8 + 2a + 19a + 3a2 + -5a2 + -10a2 = 0

Combine like terms: 2a + 19a = 21a
-8 + 21a + 3a2 + -5a2 + -10a2 = 0

Combine like terms: 3a2 + -5a2 = -2a2
-8 + 21a + -2a2 + -10a2 = 0

Combine like terms: -2a2 + -10a2 = -12a2
-8 + 21a + -12a2 = 0

Solving
-8 + 21a + -12a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
0.6666666667 + -1.75a + a2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -1.75a + -0.6666666667 + a2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -1.75a + a2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -1.75a + a2 = 0 + -0.6666666667
-1.75a + a2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-1.75a + a2 = -0.6666666667

The a term is -1.75a.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75a + 0.765625 + a2 = -0.6666666667 + 0.765625

Reorder the terms:
0.765625 + -1.75a + a2 = -0.6666666667 + 0.765625

Combine like terms: -0.6666666667 + 0.765625 = 0.0989583333
0.765625 + -1.75a + a2 = 0.0989583333

Factor a perfect square on the left side:
(a + -0.875)(a + -0.875) = 0.0989583333

Calculate the square root of the right side: 0.314576435

Break this problem into two subproblems by setting 
(a + -0.875) equal to 0.314576435 and -0.314576435.


Subproblem 1
a + -0.875 = 0.314576435

Simplifying
a + -0.875 = 0.314576435

Reorder the terms:
-0.875 + a = 0.314576435

Solving
-0.875 + a = 0.314576435

Solving for variable 'a'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + a = 0.314576435 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + a = 0.314576435 + 0.875
a = 0.314576435 + 0.875

Combine like terms: 0.314576435 + 0.875 = 1.189576435
a = 1.189576435

Simplifying
a = 1.189576435


Subproblem 2
a + -0.875 = -0.314576435

Simplifying
a + -0.875 = -0.314576435

Reorder the terms:
-0.875 + a = -0.314576435

Solving
-0.875 + a = -0.314576435

Solving for variable 'a'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + a = -0.314576435 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + a = -0.314576435 + 0.875
a = -0.314576435 + 0.875

Combine like terms: -0.314576435 + 0.875 = 0.560423565
a = 0.560423565

Simplifying
a = 0.560423565


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.189576435, 0.560423565}

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