5t-1=t*t-(t+2)(t-2)

Solution for 5t-1=t*t-(t+2)(t-2) equation:

Simplifying
5t + -1 = t * t + -1(t + 2)(t + -2)

Reorder the terms:
-1 + 5t = t * t + -1(t + 2)(t + -2)

Multiply t * t
-1 + 5t = t2 + -1(t + 2)(t + -2)

Reorder the terms:
-1 + 5t = t2 + -1(2 + t)(t + -2)

Reorder the terms:
-1 + 5t = t2 + -1(2 + t)(-2 + t)

Multiply (2 + t) * (-2 + t)
-1 + 5t = t2 + -1(2(-2 + t) + t(-2 + t))
-1 + 5t = t2 + -1((-2 * 2 + t * 2) + t(-2 + t))
-1 + 5t = t2 + -1((-4 + 2t) + t(-2 + t))
-1 + 5t = t2 + -1(-4 + 2t + (-2 * t + t * t))
-1 + 5t = t2 + -1(-4 + 2t + (-2t + t2))

Combine like terms: 2t + -2t = 0
-1 + 5t = t2 + -1(-4 + 0 + t2)
-1 + 5t = t2 + -1(-4 + t2)
-1 + 5t = t2 + (-4 * -1 + t2 * -1)
-1 + 5t = t2 + (4 + -1t2)

Reorder the terms:
-1 + 5t = 4 + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-1 + 5t = 4 + 0
-1 + 5t = 4

Solving
-1 + 5t = 4

Solving for variable 't'.

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 = 4 + 1

Combine like terms: -1 + 1 = 0
0 + 5t = 4 + 1
5t = 4 + 1

Combine like terms: 4 + 1 = 5
5t = 5

Divide each side by '5'.
t = 1

Simplifying
t = 1