7t^2+2t=5t^2+4

Solution for 7t^2+2t=5t^2+4 equation:

Simplifying
7t2 + 2t = 5t2 + 4

Reorder the terms:
2t + 7t2 = 5t2 + 4

Reorder the terms:
2t + 7t2 = 4 + 5t2

Solving
2t + 7t2 = 4 + 5t2

Solving for variable 't'.

Reorder the terms:
-4 + 2t + 7t2 + -5t2 = 4 + 5t2 + -4 + -5t2

Combine like terms: 7t2 + -5t2 = 2t2
-4 + 2t + 2t2 = 4 + 5t2 + -4 + -5t2

Reorder the terms:
-4 + 2t + 2t2 = 4 + -4 + 5t2 + -5t2

Combine like terms: 4 + -4 = 0
-4 + 2t + 2t2 = 0 + 5t2 + -5t2
-4 + 2t + 2t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-4 + 2t + 2t2 = 0

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

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

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

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

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

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

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

Simplifying
t = -2
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 = {-2, 1}