100=4t^2-24t+36

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Solution for 100=4t^2-24t+36 equation: 


Simplifying
100 = 4t2 + -24t + 36

Reorder the terms:
100 = 36 + -24t + 4t2

Solving
100 = 36 + -24t + 4t2

Solving for variable 't'.

Combine like terms: 100 + -36 = 64
64 + 24t + -4t2 = 36 + -24t + 4t2 + -36 + 24t + -4t2

Reorder the terms:
64 + 24t + -4t2 = 36 + -36 + -24t + 24t + 4t2 + -4t2

Combine like terms: 36 + -36 = 0
64 + 24t + -4t2 = 0 + -24t + 24t + 4t2 + -4t2
64 + 24t + -4t2 = -24t + 24t + 4t2 + -4t2

Combine like terms: -24t + 24t = 0
64 + 24t + -4t2 = 0 + 4t2 + -4t2
64 + 24t + -4t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
64 + 24t + -4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + 6t + -1t2) = 0

Factor a trinomial.
4((8 + -1t)(2 + t)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8

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

Simplifying
2 + t = 0

Solving
2 + t = 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 + t = 0 + -2

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

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

Simplifying
t = -2
Solution
t = {8, -2}

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