13-(4a-1)=(4a+7)(7-4a)-37

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Solution for 13-(4a-1)=(4a+7)(7-4a)-37 equation: 


Simplifying
13 + -1(4a + -1) = (4a + 7)(7 + -4a) + -37

Reorder the terms:
13 + -1(-1 + 4a) = (4a + 7)(7 + -4a) + -37
13 + (-1 * -1 + 4a * -1) = (4a + 7)(7 + -4a) + -37
13 + (1 + -4a) = (4a + 7)(7 + -4a) + -37

Combine like terms: 13 + 1 = 14
14 + -4a = (4a + 7)(7 + -4a) + -37

Reorder the terms:
14 + -4a = (7 + 4a)(7 + -4a) + -37

Multiply (7 + 4a) * (7 + -4a)
14 + -4a = (7(7 + -4a) + 4a * (7 + -4a)) + -37
14 + -4a = ((7 * 7 + -4a * 7) + 4a * (7 + -4a)) + -37
14 + -4a = ((49 + -28a) + 4a * (7 + -4a)) + -37
14 + -4a = (49 + -28a + (7 * 4a + -4a * 4a)) + -37
14 + -4a = (49 + -28a + (28a + -16a2)) + -37

Combine like terms: -28a + 28a = 0
14 + -4a = (49 + 0 + -16a2) + -37
14 + -4a = (49 + -16a2) + -37

Reorder the terms:
14 + -4a = 49 + -37 + -16a2

Combine like terms: 49 + -37 = 12
14 + -4a = 12 + -16a2

Solving
14 + -4a = 12 + -16a2

Solving for variable 'a'.

Reorder the terms:
14 + -12 + -4a + 16a2 = 12 + -16a2 + -12 + 16a2

Combine like terms: 14 + -12 = 2
2 + -4a + 16a2 = 12 + -16a2 + -12 + 16a2

Reorder the terms:
2 + -4a + 16a2 = 12 + -12 + -16a2 + 16a2

Combine like terms: 12 + -12 = 0
2 + -4a + 16a2 = 0 + -16a2 + 16a2
2 + -4a + 16a2 = -16a2 + 16a2

Combine like terms: -16a2 + 16a2 = 0
2 + -4a + 16a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2a + 8a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -2a + 8a2)' equal to zero and attempt to solve:

Simplifying
1 + -2a + 8a2 = 0

Solving
1 + -2a + 8a2 = 0

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

Divide each side by '8'.
0.125 + -0.25a + a2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -0.25a + -0.125 + a2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -0.25a + a2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -0.25a + a2 = 0 + -0.125
-0.25a + a2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-0.25a + a2 = -0.125

The a term is -0.25a.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25a + 0.015625 + a2 = -0.125 + 0.015625

Reorder the terms:
0.015625 + -0.25a + a2 = -0.125 + 0.015625

Combine like terms: -0.125 + 0.015625 = -0.109375
0.015625 + -0.25a + a2 = -0.109375

Factor a perfect square on the left side:
(a + -0.125)(a + -0.125) = -0.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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