(2a-14)(a+28)=360

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Solution for (2a-14)(a+28)=360 equation: 


Simplifying
(2a + -14)(a + 28) = 360

Reorder the terms:
(-14 + 2a)(a + 28) = 360

Reorder the terms:
(-14 + 2a)(28 + a) = 360

Multiply (-14 + 2a) * (28 + a)
(-14(28 + a) + 2a * (28 + a)) = 360
((28 * -14 + a * -14) + 2a * (28 + a)) = 360
((-392 + -14a) + 2a * (28 + a)) = 360
(-392 + -14a + (28 * 2a + a * 2a)) = 360
(-392 + -14a + (56a + 2a2)) = 360

Combine like terms: -14a + 56a = 42a
(-392 + 42a + 2a2) = 360

Solving
-392 + 42a + 2a2 = 360

Solving for variable 'a'.

Reorder the terms:
-392 + -360 + 42a + 2a2 = 360 + -360

Combine like terms: -392 + -360 = -752
-752 + 42a + 2a2 = 360 + -360

Combine like terms: 360 + -360 = 0
-752 + 42a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-376 + 21a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-376 + 21a + a2)' equal to zero and attempt to solve:

Simplifying
-376 + 21a + a2 = 0

Solving
-376 + 21a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '376' to each side of the equation.
-376 + 21a + 376 + a2 = 0 + 376

Reorder the terms:
-376 + 376 + 21a + a2 = 0 + 376

Combine like terms: -376 + 376 = 0
0 + 21a + a2 = 0 + 376
21a + a2 = 0 + 376

Combine like terms: 0 + 376 = 376
21a + a2 = 376

The a term is 21a.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21a + 110.25 + a2 = 376 + 110.25

Reorder the terms:
110.25 + 21a + a2 = 376 + 110.25

Combine like terms: 376 + 110.25 = 486.25
110.25 + 21a + a2 = 486.25

Factor a perfect square on the left side:
(a + 10.5)(a + 10.5) = 486.25

Calculate the square root of the right side: 22.051077071

Break this problem into two subproblems by setting 
(a + 10.5) equal to 22.051077071 and -22.051077071.


Subproblem 1
a + 10.5 = 22.051077071

Simplifying
a + 10.5 = 22.051077071

Reorder the terms:
10.5 + a = 22.051077071

Solving
10.5 + a = 22.051077071

Solving for variable 'a'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + a = 22.051077071 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + a = 22.051077071 + -10.5
a = 22.051077071 + -10.5

Combine like terms: 22.051077071 + -10.5 = 11.551077071
a = 11.551077071

Simplifying
a = 11.551077071


Subproblem 2
a + 10.5 = -22.051077071

Simplifying
a + 10.5 = -22.051077071

Reorder the terms:
10.5 + a = -22.051077071

Solving
10.5 + a = -22.051077071

Solving for variable 'a'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + a = -22.051077071 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + a = -22.051077071 + -10.5
a = -22.051077071 + -10.5

Combine like terms: -22.051077071 + -10.5 = -32.551077071
a = -32.551077071

Simplifying
a = -32.551077071


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {11.551077071, -32.551077071}
Solution
a = {11.551077071, -32.551077071}

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