15t^2-7t=2

Solution for 15t^2-7t=2 equation:

Simplifying
15t2 + -7t = 2

Reorder the terms:
-7t + 15t2 = 2

Solving
-7t + 15t2 = 2

Solving for variable 't'.

Reorder the terms:
-2 + -7t + 15t2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -7t + 15t2 = 0

Factor a trinomial.
(-1 + -5t)(2 + -3t) = 0

Subproblem 1
Set the factor '(-1 + -5t)' equal to zero and attempt to solve:

Simplifying
-1 + -5t = 0

Solving
-1 + -5t = 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 + -5t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5t = 0 + 1
-5t = 0 + 1

Combine like terms: 0 + 1 = 1
-5t = 1

Divide each side by '-5'.
t = -0.2

Simplifying
t = -0.2
Subproblem 2
Set the factor '(2 + -3t)' equal to zero and attempt to solve:

Simplifying
2 + -3t = 0

Solving
2 + -3t = 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 + -3t = 0 + -2

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

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

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Solution
t = {-0.2, 0.6666666667}