(t-6)(t+6)-45=0

Solution for (t-6)(t+6)-45=0 equation:

Simplifying
(t + -6)(t + 6) + -45 = 0

Reorder the terms:
(-6 + t)(t + 6) + -45 = 0

Reorder the terms:
(-6 + t)(6 + t) + -45 = 0

Multiply (-6 + t) * (6 + t)
(-6(6 + t) + t(6 + t)) + -45 = 0
((6 * -6 + t * -6) + t(6 + t)) + -45 = 0
((-36 + -6t) + t(6 + t)) + -45 = 0
(-36 + -6t + (6 * t + t * t)) + -45 = 0
(-36 + -6t + (6t + t2)) + -45 = 0

Combine like terms: -6t + 6t = 0
(-36 + 0 + t2) + -45 = 0
(-36 + t2) + -45 = 0

Reorder the terms:
-36 + -45 + t2 = 0

Combine like terms: -36 + -45 = -81
-81 + t2 = 0

Solving
-81 + t2 = 0

Solving for variable 't'.

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

Add '81' to each side of the equation.
-81 + 81 + t2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + t2 = 0 + 81
t2 = 0 + 81

Combine like terms: 0 + 81 = 81
t2 = 81

Simplifying
t2 = 81

Take the square root of each side:
t = {-9, 9}