364=4t^2-53t+188

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Solution for 364=4t^2-53t+188 equation: 


Simplifying
364 = 4t2 + -53t + 188

Reorder the terms:
364 = 188 + -53t + 4t2

Solving
364 = 188 + -53t + 4t2

Solving for variable 't'.

Combine like terms: 364 + -188 = 176
176 + 53t + -4t2 = 188 + -53t + 4t2 + -188 + 53t + -4t2

Reorder the terms:
176 + 53t + -4t2 = 188 + -188 + -53t + 53t + 4t2 + -4t2

Combine like terms: 188 + -188 = 0
176 + 53t + -4t2 = 0 + -53t + 53t + 4t2 + -4t2
176 + 53t + -4t2 = -53t + 53t + 4t2 + -4t2

Combine like terms: -53t + 53t = 0
176 + 53t + -4t2 = 0 + 4t2 + -4t2
176 + 53t + -4t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
176 + 53t + -4t2 = 0

Factor a trinomial.
(16 + -1t)(11 + 4t) = 0


Subproblem 1
Set the factor '(16 + -1t)' equal to zero and attempt to solve:

Simplifying
16 + -1t = 0

Solving
16 + -1t = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1t = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1t = 0 + -16
-1t = 0 + -16

Combine like terms: 0 + -16 = -16
-1t = -16

Divide each side by '-1'.
t = 16

Simplifying
t = 16

Subproblem 2
Set the factor '(11 + 4t)' equal to zero and attempt to solve:

Simplifying
11 + 4t = 0

Solving
11 + 4t = 0

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

Add '-11' to each side of the equation.
11 + -11 + 4t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 4t = 0 + -11
4t = 0 + -11

Combine like terms: 0 + -11 = -11
4t = -11

Divide each side by '4'.
t = -2.75

Simplifying
t = -2.75
Solution
t = {16, -2.75}

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