x^2+(1-t)x+(2t-6)=0

Solution for x^2+(1-t)x+(2t-6)=0 equation:

Simplifying
x2 + (1 + -1t) * x + (2t + -6) = 0

Reorder the terms for easier multiplication:
x2 + x(1 + -1t) + (2t + -6) = 0
x2 + (1 * x + -1t * x) + (2t + -6) = 0

Reorder the terms:
x2 + (-1tx + 1x) + (2t + -6) = 0
x2 + (-1tx + 1x) + (2t + -6) = 0

Reorder the terms:
x2 + -1tx + 1x + (-6 + 2t) = 0

Remove parenthesis around (-6 + 2t)
x2 + -1tx + 1x + -6 + 2t = 0

Reorder the terms:
-6 + 2t + -1tx + 1x + x2 = 0

Solving
-6 + 2t + -1tx + 1x + x2 = 0

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 2t + -1tx + 1x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 2t + -1tx + 1x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2t + -1tx + 1x + x2 = 0 + 6
2t + -1tx + 1x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
2t + -1tx + 1x + x2 = 6

Add '-1x' to each side of the equation.
2t + -1tx + 1x + -1x + x2 = 6 + -1x

Combine like terms: 1x + -1x = 0
2t + -1tx + 0 + x2 = 6 + -1x
2t + -1tx + x2 = 6 + -1x

Add '-1x2' to each side of the equation.
2t + -1tx + x2 + -1x2 = 6 + -1x + -1x2

Combine like terms: x2 + -1x2 = 0
2t + -1tx + 0 = 6 + -1x + -1x2
2t + -1tx = 6 + -1x + -1x2

Reorder the terms:
-6 + 2t + -1tx + x + x2 = 6 + -1x + -1x2 + -6 + x + x2

Reorder the terms:
-6 + 2t + -1tx + x + x2 = 6 + -6 + -1x + x + -1x2 + x2

Combine like terms: 6 + -6 = 0
-6 + 2t + -1tx + x + x2 = 0 + -1x + x + -1x2 + x2
-6 + 2t + -1tx + x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-6 + 2t + -1tx + x + x2 = 0 + -1x2 + x2
-6 + 2t + -1tx + x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-6 + 2t + -1tx + x + x2 = 0

The solution to this equation could not be determined.