t^2-4=2t(t-2)(-5)

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Solution for t^2-4=2t(t-2)(-5) equation: 


Simplifying
t2 + -4 = 2t(t + -2)(-5)

Reorder the terms:
-4 + t2 = 2t(t + -2)(-5)

Reorder the terms:
-4 + t2 = 2t(-2 + t)(-5)

Reorder the terms for easier multiplication:
-4 + t2 = 2 * -5t(-2 + t)

Multiply 2 * -5
-4 + t2 = -10t(-2 + t)
-4 + t2 = (-2 * -10t + t * -10t)
-4 + t2 = (20t + -10t2)

Solving
-4 + t2 = 20t + -10t2

Solving for variable 't'.

Reorder the terms:
-4 + -20t + t2 + 10t2 = 20t + -10t2 + -20t + 10t2

Combine like terms: t2 + 10t2 = 11t2
-4 + -20t + 11t2 = 20t + -10t2 + -20t + 10t2

Reorder the terms:
-4 + -20t + 11t2 = 20t + -20t + -10t2 + 10t2

Combine like terms: 20t + -20t = 0
-4 + -20t + 11t2 = 0 + -10t2 + 10t2
-4 + -20t + 11t2 = -10t2 + 10t2

Combine like terms: -10t2 + 10t2 = 0
-4 + -20t + 11t2 = 0

Factor a trinomial.
(-2 + -11t)(2 + -1t) = 0


Subproblem 1
Set the factor '(-2 + -11t)' equal to zero and attempt to solve:

Simplifying
-2 + -11t = 0

Solving
-2 + -11t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -11t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -11t = 0 + 2
-11t = 0 + 2

Combine like terms: 0 + 2 = 2
-11t = 2

Divide each side by '-11'.
t = -0.1818181818

Simplifying
t = -0.1818181818

Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-0.1818181818, 2}

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