0=4(4t^2-16t+7)

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Solution for 0=4(4t^2-16t+7) equation: 


Simplifying
0 = 4(4t2 + -16t + 7)

Reorder the terms:
0 = 4(7 + -16t + 4t2)
0 = (7 * 4 + -16t * 4 + 4t2 * 4)
0 = (28 + -64t + 16t2)

Solving
0 = 28 + -64t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -28 = -28
-28 + 64t + -16t2 = 28 + -64t + 16t2 + -28 + 64t + -16t2

Reorder the terms:
-28 + 64t + -16t2 = 28 + -28 + -64t + 64t + 16t2 + -16t2

Combine like terms: 28 + -28 = 0
-28 + 64t + -16t2 = 0 + -64t + 64t + 16t2 + -16t2
-28 + 64t + -16t2 = -64t + 64t + 16t2 + -16t2

Combine like terms: -64t + 64t = 0
-28 + 64t + -16t2 = 0 + 16t2 + -16t2
-28 + 64t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-28 + 64t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 16t + -4t2) = 0

Factor a trinomial.
4((-7 + 2t)(1 + -2t)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + 2t)' equal to zero and attempt to solve:

Simplifying
-7 + 2t = 0

Solving
-7 + 2t = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2t = 0 + 7
2t = 0 + 7

Combine like terms: 0 + 7 = 7
2t = 7

Divide each side by '2'.
t = 3.5

Simplifying
t = 3.5

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

Simplifying
1 + -2t = 0

Solving
1 + -2t = 0

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

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

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {3.5, 0.5}

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