(2u+4ta)(u+ta)=

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Solution for (2u+4ta)(u+ta)= equation: 


Simplifying
(2u + 4ta)(u + ta) = 0

Reorder the terms:
(4at + 2u)(u + ta) = 0

Reorder the terms:
(4at + 2u)(at + u) = 0

Multiply (4at + 2u) * (at + u)
(4at * (at + u) + 2u * (at + u)) = 0
((at * 4at + u * 4at) + 2u * (at + u)) = 0

Reorder the terms:
((4atu + 4a2t2) + 2u * (at + u)) = 0
((4atu + 4a2t2) + 2u * (at + u)) = 0
(4atu + 4a2t2 + (at * 2u + u * 2u)) = 0
(4atu + 4a2t2 + (2atu + 2u2)) = 0

Reorder the terms:
(4atu + 2atu + 4a2t2 + 2u2) = 0

Combine like terms: 4atu + 2atu = 6atu
(6atu + 4a2t2 + 2u2) = 0

Solving
6atu + 4a2t2 + 2u2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3atu + 2a2t2 + u2) = 0

Factor a trinomial.
2((2at + u)(at + u)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2at + u)' equal to zero and attempt to solve:

Simplifying
2at + u = 0

Solving
2at + u = 0

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

Add '-1u' to each side of the equation.
2at + u + -1u = 0 + -1u

Combine like terms: u + -1u = 0
2at + 0 = 0 + -1u
2at = 0 + -1u
Remove the zero:
2at = -1u

Divide each side by '2t'.
a = -0.5t-1u

Simplifying
a = -0.5t-1u

Subproblem 2
Set the factor '(at + u)' equal to zero and attempt to solve:

Simplifying
at + u = 0

Solving
at + u = 0

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

Add '-1u' to each side of the equation.
at + u + -1u = 0 + -1u

Combine like terms: u + -1u = 0
at + 0 = 0 + -1u
at = 0 + -1u
Remove the zero:
at = -1u

Divide each side by 't'.
a = -1t-1u

Simplifying
a = -1t-1u
Solution
a = {-0.5t-1u, -1t-1u}

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