4x^2-4xt-3t^2=0

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Solution for 4x^2-4xt-3t^2=0 equation: 


Simplifying
4x2 + -4xt + -3t2 = 0

Reorder the terms:
-4tx + -3t2 + 4x2 = 0

Solving
-4tx + -3t2 + 4x2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1t + -2x)(3t + -2x) = 0


Subproblem 1
Set the factor '(-1t + -2x)' equal to zero and attempt to solve:

Simplifying
-1t + -2x = 0

Solving
-1t + -2x = 0

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

Add '2x' to each side of the equation.
-1t + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
-1t + 0 = 0 + 2x
-1t = 0 + 2x
Remove the zero:
-1t = 2x

Divide each side by '-1'.
t = -2x

Simplifying
t = -2x

Subproblem 2
Set the factor '(3t + -2x)' equal to zero and attempt to solve:

Simplifying
3t + -2x = 0

Solving
3t + -2x = 0

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

Add '2x' to each side of the equation.
3t + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
3t + 0 = 0 + 2x
3t = 0 + 2x
Remove the zero:
3t = 2x

Divide each side by '3'.
t = 0.6666666667x

Simplifying
t = 0.6666666667x
Solution
t = {-2x, 0.6666666667x}

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