42t^2-17t=15

Solution for 42t^2-17t=15 equation:

Simplifying
42t2 + -17t = 15

Reorder the terms:
-17t + 42t2 = 15

Solving
-17t + 42t2 = 15

Solving for variable 't'.

Reorder the terms:
-15 + -17t + 42t2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -17t + 42t2 = 0

Factor a trinomial.
(-3 + -7t)(5 + -6t) = 0

Subproblem 1
Set the factor '(-3 + -7t)' equal to zero and attempt to solve:

Simplifying
-3 + -7t = 0

Solving
-3 + -7t = 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 + -7t = 0 + 3

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

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

Divide each side by '-7'.
t = -0.4285714286

Simplifying
t = -0.4285714286
Subproblem 2
Set the factor '(5 + -6t)' equal to zero and attempt to solve:

Simplifying
5 + -6t = 0

Solving
5 + -6t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6t = 0 + -5
-6t = 0 + -5

Combine like terms: 0 + -5 = -5
-6t = -5

Divide each side by '-6'.
t = 0.8333333333

Simplifying
t = 0.8333333333
Solution
t = {-0.4285714286, 0.8333333333}