2t^2+3t-4=2t-1

Solution for 2t^2+3t-4=2t-1 equation:

Simplifying
2t2 + 3t + -4 = 2t + -1

Reorder the terms:
-4 + 3t + 2t2 = 2t + -1

Reorder the terms:
-4 + 3t + 2t2 = -1 + 2t

Solving
-4 + 3t + 2t2 = -1 + 2t

Solving for variable 't'.

Reorder the terms:
-4 + 1 + 3t + -2t + 2t2 = -1 + 2t + 1 + -2t

Combine like terms: -4 + 1 = -3
-3 + 3t + -2t + 2t2 = -1 + 2t + 1 + -2t

Combine like terms: 3t + -2t = 1t
-3 + 1t + 2t2 = -1 + 2t + 1 + -2t

Reorder the terms:
-3 + 1t + 2t2 = -1 + 1 + 2t + -2t

Combine like terms: -1 + 1 = 0
-3 + 1t + 2t2 = 0 + 2t + -2t
-3 + 1t + 2t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-3 + 1t + 2t2 = 0

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

Subproblem 1
Set the factor '(-3 + -2t)' equal to zero and attempt to solve:

Simplifying
-3 + -2t = 0

Solving
-3 + -2t = 0

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

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

Combine like terms: -3 + 3 = 0
0 + -2t = 0 + 3
-2t = 0 + 3

Combine like terms: 0 + 3 = 3
-2t = 3

Divide each side by '-2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

Simplifying
t = 1
Solution
t = {-1.5, 1}