(2a+4)(2a-10)-(a+4)(a+3)=

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Solution for (2a+4)(2a-10)-(a+4)(a+3)= equation: 


Simplifying
(2a + 4)(2a + -10) + -1(a + 4)(a + 3) = 0

Reorder the terms:
(4 + 2a)(2a + -10) + -1(a + 4)(a + 3) = 0

Reorder the terms:
(4 + 2a)(-10 + 2a) + -1(a + 4)(a + 3) = 0

Multiply (4 + 2a) * (-10 + 2a)
(4(-10 + 2a) + 2a * (-10 + 2a)) + -1(a + 4)(a + 3) = 0
((-10 * 4 + 2a * 4) + 2a * (-10 + 2a)) + -1(a + 4)(a + 3) = 0
((-40 + 8a) + 2a * (-10 + 2a)) + -1(a + 4)(a + 3) = 0
(-40 + 8a + (-10 * 2a + 2a * 2a)) + -1(a + 4)(a + 3) = 0
(-40 + 8a + (-20a + 4a2)) + -1(a + 4)(a + 3) = 0

Combine like terms: 8a + -20a = -12a
(-40 + -12a + 4a2) + -1(a + 4)(a + 3) = 0

Reorder the terms:
-40 + -12a + 4a2 + -1(4 + a)(a + 3) = 0

Reorder the terms:
-40 + -12a + 4a2 + -1(4 + a)(3 + a) = 0

Multiply (4 + a) * (3 + a)
-40 + -12a + 4a2 + -1(4(3 + a) + a(3 + a)) = 0
-40 + -12a + 4a2 + -1((3 * 4 + a * 4) + a(3 + a)) = 0
-40 + -12a + 4a2 + -1((12 + 4a) + a(3 + a)) = 0
-40 + -12a + 4a2 + -1(12 + 4a + (3 * a + a * a)) = 0
-40 + -12a + 4a2 + -1(12 + 4a + (3a + a2)) = 0

Combine like terms: 4a + 3a = 7a
-40 + -12a + 4a2 + -1(12 + 7a + a2) = 0
-40 + -12a + 4a2 + (12 * -1 + 7a * -1 + a2 * -1) = 0
-40 + -12a + 4a2 + (-12 + -7a + -1a2) = 0

Reorder the terms:
-40 + -12 + -12a + -7a + 4a2 + -1a2 = 0

Combine like terms: -40 + -12 = -52
-52 + -12a + -7a + 4a2 + -1a2 = 0

Combine like terms: -12a + -7a = -19a
-52 + -19a + 4a2 + -1a2 = 0

Combine like terms: 4a2 + -1a2 = 3a2
-52 + -19a + 3a2 = 0

Solving
-52 + -19a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-17.33333333 + -6.333333333a + a2 = 0

Move the constant term to the right:

Add '17.33333333' to each side of the equation.
-17.33333333 + -6.333333333a + 17.33333333 + a2 = 0 + 17.33333333

Reorder the terms:
-17.33333333 + 17.33333333 + -6.333333333a + a2 = 0 + 17.33333333

Combine like terms: -17.33333333 + 17.33333333 = 0.00000000
0.00000000 + -6.333333333a + a2 = 0 + 17.33333333
-6.333333333a + a2 = 0 + 17.33333333

Combine like terms: 0 + 17.33333333 = 17.33333333
-6.333333333a + a2 = 17.33333333

The a term is -6.333333333a.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333a + 10.02777778 + a2 = 17.33333333 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333a + a2 = 17.33333333 + 10.02777778

Combine like terms: 17.33333333 + 10.02777778 = 27.36111111
10.02777778 + -6.333333333a + a2 = 27.36111111

Factor a perfect square on the left side:
(a + -3.166666667)(a + -3.166666667) = 27.36111111

Calculate the square root of the right side: 5.230784942

Break this problem into two subproblems by setting 
(a + -3.166666667) equal to 5.230784942 and -5.230784942.


Subproblem 1
a + -3.166666667 = 5.230784942

Simplifying
a + -3.166666667 = 5.230784942

Reorder the terms:
-3.166666667 + a = 5.230784942

Solving
-3.166666667 + a = 5.230784942

Solving for variable 'a'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + a = 5.230784942 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + a = 5.230784942 + 3.166666667
a = 5.230784942 + 3.166666667

Combine like terms: 5.230784942 + 3.166666667 = 8.397451609
a = 8.397451609

Simplifying
a = 8.397451609


Subproblem 2
a + -3.166666667 = -5.230784942

Simplifying
a + -3.166666667 = -5.230784942

Reorder the terms:
-3.166666667 + a = -5.230784942

Solving
-3.166666667 + a = -5.230784942

Solving for variable 'a'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + a = -5.230784942 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + a = -5.230784942 + 3.166666667
a = -5.230784942 + 3.166666667

Combine like terms: -5.230784942 + 3.166666667 = -2.064118275
a = -2.064118275

Simplifying
a = -2.064118275


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {8.397451609, -2.064118275}

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