15t^2+t-6=(t+3)(t-2)

Solution for 15t^2+t-6=(t+3)(t-2) equation:

Simplifying
15t2 + t + -6 = (t + 3)(t + -2)

Reorder the terms:
-6 + t + 15t2 = (t + 3)(t + -2)

Reorder the terms:
-6 + t + 15t2 = (3 + t)(t + -2)

Reorder the terms:
-6 + t + 15t2 = (3 + t)(-2 + t)

Multiply (3 + t) * (-2 + t)
-6 + t + 15t2 = (3(-2 + t) + t(-2 + t))
-6 + t + 15t2 = ((-2 * 3 + t * 3) + t(-2 + t))
-6 + t + 15t2 = ((-6 + 3t) + t(-2 + t))
-6 + t + 15t2 = (-6 + 3t + (-2 * t + t * t))
-6 + t + 15t2 = (-6 + 3t + (-2t + t2))

Combine like terms: 3t + -2t = 1t
-6 + t + 15t2 = (-6 + 1t + t2)

Add '6' to each side of the equation.
-6 + t + 6 + 15t2 = -6 + 1t + 6 + t2

Reorder the terms:
-6 + 6 + t + 15t2 = -6 + 1t + 6 + t2

Combine like terms: -6 + 6 = 0
0 + t + 15t2 = -6 + 1t + 6 + t2
t + 15t2 = -6 + 1t + 6 + t2

Reorder the terms:
t + 15t2 = -6 + 6 + 1t + t2

Combine like terms: -6 + 6 = 0
t + 15t2 = 0 + 1t + t2
t + 15t2 = 1t + t2

Solving
t + 15t2 = 1t + t2

Solving for variable 't'.

Reorder the terms:
t + -1t + 15t2 + -1t2 = 1t + t2 + -1t + -1t2

Combine like terms: t + -1t = 0
0 + 15t2 + -1t2 = 1t + t2 + -1t + -1t2
15t2 + -1t2 = 1t + t2 + -1t + -1t2

Combine like terms: 15t2 + -1t2 = 14t2
14t2 = 1t + t2 + -1t + -1t2

Reorder the terms:
14t2 = 1t + -1t + t2 + -1t2

Combine like terms: 1t + -1t = 0
14t2 = 0 + t2 + -1t2
14t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
14t2 = 0

Ignore the factor 14.
Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}
Solution
t = {0}