16x^2-a^2=4x+a^2

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Solution for 16x^2-a^2=4x+a^2 equation: 


Simplifying
16x2 + -1a2 = 4x + a2

Reorder the terms:
-1a2 + 16x2 = 4x + a2

Reorder the terms:
-1a2 + 16x2 = a2 + 4x

Solving
-1a2 + 16x2 = a2 + 4x

Solving for variable 'a'.

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

Add '-1a2' to each side of the equation.
-1a2 + -1a2 + 16x2 = a2 + -1a2 + 4x

Combine like terms: -1a2 + -1a2 = -2a2
-2a2 + 16x2 = a2 + -1a2 + 4x

Combine like terms: a2 + -1a2 = 0
-2a2 + 16x2 = 0 + 4x
-2a2 + 16x2 = 4x

Add '-16x2' to each side of the equation.
-2a2 + 16x2 + -16x2 = 4x + -16x2

Combine like terms: 16x2 + -16x2 = 0
-2a2 + 0 = 4x + -16x2
-2a2 = 4x + -16x2

Divide each side by '-2'.
a2 = -2x + 8x2

Simplifying
a2 = -2x + 8x2

Reorder the terms:
a2 + 2x + -8x2 = -2x + 2x + 8x2 + -8x2

Combine like terms: -2x + 2x = 0
a2 + 2x + -8x2 = 0 + 8x2 + -8x2
a2 + 2x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
a2 + 2x + -8x2 = 0

Factor a trinomial.
(a + -2x)(a + 4x) = 0


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

Simplifying
a + -2x = 0

Solving
a + -2x = 0

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

Add '2x' to each side of the equation.
a + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
a + 0 = 0 + 2x
a = 0 + 2x
Remove the zero:
a = 2x

Simplifying
a = 2x

Subproblem 2
Set the factor '(a + 4x)' equal to zero and attempt to solve:

Simplifying
a + 4x = 0

Solving
a + 4x = 0

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

Add '-4x' to each side of the equation.
a + 4x + -4x = 0 + -4x

Combine like terms: 4x + -4x = 0
a + 0 = 0 + -4x
a = 0 + -4x
Remove the zero:
a = -4x

Simplifying
a = -4x
Solution
a = {2x, -4x}

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