(t-6)(t+6)=(t-2)(t-4)

Solution for (t-6)(t+6)=(t-2)(t-4) equation:

Simplifying
(t + -6)(t + 6) = (t + -2)(t + -4)

Reorder the terms:
(-6 + t)(t + 6) = (t + -2)(t + -4)

Reorder the terms:
(-6 + t)(6 + t) = (t + -2)(t + -4)

Multiply (-6 + t) * (6 + t)
(-6(6 + t) + t(6 + t)) = (t + -2)(t + -4)
((6 * -6 + t * -6) + t(6 + t)) = (t + -2)(t + -4)
((-36 + -6t) + t(6 + t)) = (t + -2)(t + -4)
(-36 + -6t + (6 * t + t * t)) = (t + -2)(t + -4)
(-36 + -6t + (6t + t2)) = (t + -2)(t + -4)

Combine like terms: -6t + 6t = 0
(-36 + 0 + t2) = (t + -2)(t + -4)
(-36 + t2) = (t + -2)(t + -4)

Reorder the terms:
-36 + t2 = (-2 + t)(t + -4)

Reorder the terms:
-36 + t2 = (-2 + t)(-4 + t)

Multiply (-2 + t) * (-4 + t)
-36 + t2 = (-2(-4 + t) + t(-4 + t))
-36 + t2 = ((-4 * -2 + t * -2) + t(-4 + t))
-36 + t2 = ((8 + -2t) + t(-4 + t))
-36 + t2 = (8 + -2t + (-4 * t + t * t))
-36 + t2 = (8 + -2t + (-4t + t2))

Combine like terms: -2t + -4t = -6t
-36 + t2 = (8 + -6t + t2)

Add '-1t2' to each side of the equation.
-36 + t2 + -1t2 = 8 + -6t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-36 + 0 = 8 + -6t + t2 + -1t2
-36 = 8 + -6t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-36 = 8 + -6t + 0
-36 = 8 + -6t

Solving
-36 = 8 + -6t

Solving for variable 't'.

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

Add '6t' to each side of the equation.
-36 + 6t = 8 + -6t + 6t

Combine like terms: -6t + 6t = 0
-36 + 6t = 8 + 0
-36 + 6t = 8

Add '36' to each side of the equation.
-36 + 36 + 6t = 8 + 36

Combine like terms: -36 + 36 = 0
0 + 6t = 8 + 36
6t = 8 + 36

Combine like terms: 8 + 36 = 44
6t = 44

Divide each side by '6'.
t = 7.333333333

Simplifying
t = 7.333333333