.75(t^2+1)=(t^2-t+1)

Solution for .75(t^2+1)=(t^2-t+1) equation:

Simplifying
0.75(t2 + 1) = (t2 + -1t + 1)

Reorder the terms:
0.75(1 + t2) = (t2 + -1t + 1)
(1 * 0.75 + t2 * 0.75) = (t2 + -1t + 1)
(0.75 + 0.75t2) = (t2 + -1t + 1)

Reorder the terms:
0.75 + 0.75t2 = (1 + -1t + t2)

Remove parenthesis around (1 + -1t + t2)
0.75 + 0.75t2 = 1 + -1t + t2

Solving
0.75 + 0.75t2 = 1 + -1t + t2

Solving for variable 't'.

Reorder the terms:
0.75 + -1 + t + 0.75t2 + -1t2 = 1 + -1t + t2 + -1 + t + -1t2

Combine like terms: 0.75 + -1 = -0.25
-0.25 + t + 0.75t2 + -1t2 = 1 + -1t + t2 + -1 + t + -1t2

Combine like terms: 0.75t2 + -1t2 = -0.25t2
-0.25 + t + -0.25t2 = 1 + -1t + t2 + -1 + t + -1t2

Reorder the terms:
-0.25 + t + -0.25t2 = 1 + -1 + -1t + t + t2 + -1t2

Combine like terms: 1 + -1 = 0
-0.25 + t + -0.25t2 = 0 + -1t + t + t2 + -1t2
-0.25 + t + -0.25t2 = -1t + t + t2 + -1t2

Combine like terms: -1t + t = 0
-0.25 + t + -0.25t2 = 0 + t2 + -1t2
-0.25 + t + -0.25t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-0.25 + t + -0.25t2 = 0

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
1 + -4t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -4t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t + t2 = 0 + -1
-4t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4t + t2 = -1

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-4t + 0.25 + t2 = -1 + 0.25

Reorder the terms:
0.25 + -4t + t2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + -4t + t2 = -0.75

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.