252=-16t^2+14t+288

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Solution for 252=-16t^2+14t+288 equation: 


Simplifying
252 = -16t2 + 14t + 288

Reorder the terms:
252 = 288 + 14t + -16t2

Solving
252 = 288 + 14t + -16t2

Solving for variable 't'.

Combine like terms: 252 + -288 = -36
-36 + -14t + 16t2 = 288 + 14t + -16t2 + -288 + -14t + 16t2

Reorder the terms:
-36 + -14t + 16t2 = 288 + -288 + 14t + -14t + -16t2 + 16t2

Combine like terms: 288 + -288 = 0
-36 + -14t + 16t2 = 0 + 14t + -14t + -16t2 + 16t2
-36 + -14t + 16t2 = 14t + -14t + -16t2 + 16t2

Combine like terms: 14t + -14t = 0
-36 + -14t + 16t2 = 0 + -16t2 + 16t2
-36 + -14t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-36 + -14t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -7t + 8t2) = 0

Factor a trinomial.
2((-9 + -8t)(2 + -1t)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -8t)' equal to zero and attempt to solve:

Simplifying
-9 + -8t = 0

Solving
-9 + -8t = 0

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

Add '9' to each side of the equation.
-9 + 9 + -8t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -8t = 0 + 9
-8t = 0 + 9

Combine like terms: 0 + 9 = 9
-8t = 9

Divide each side by '-8'.
t = -1.125

Simplifying
t = -1.125

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 = {-1.125, 2}

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