-2t^2=7t+3

Solution for -2t^2=7t+3 equation:

Simplifying
-2t2 = 7t + 3

Reorder the terms:
-2t2 = 3 + 7t

Solving
-2t2 = 3 + 7t

Solving for variable 't'.

Reorder the terms:
-3 + -7t + -2t2 = 3 + 7t + -3 + -7t

Reorder the terms:
-3 + -7t + -2t2 = 3 + -3 + 7t + -7t

Combine like terms: 3 + -3 = 0
-3 + -7t + -2t2 = 0 + 7t + -7t
-3 + -7t + -2t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
-3 + -7t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7t + 2t2) = 0

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

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

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

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

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

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

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

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

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

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {-3, -0.5}