4((2+-1t)(1+4t))=0

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Solution for 4((2+-1t)(1+4t))=0 equation: 


Simplifying
4((2 + -1t)(1 + 4t)) = 0

Multiply (2 + -1t) * (1 + 4t)
4((2(1 + 4t) + -1t * (1 + 4t))) = 0
4(((1 * 2 + 4t * 2) + -1t * (1 + 4t))) = 0
4(((2 + 8t) + -1t * (1 + 4t))) = 0
4((2 + 8t + (1 * -1t + 4t * -1t))) = 0
4((2 + 8t + (-1t + -4t2))) = 0

Combine like terms: 8t + -1t = 7t
4((2 + 7t + -4t2)) = 0
(2 * 4 + 7t * 4 + -4t2 * 4) = 0
(8 + 28t + -16t2) = 0

Solving
8 + 28t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 7t + -4t2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + 4t)' equal to zero and attempt to solve:

Simplifying
1 + 4t = 0

Solving
1 + 4t = 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 + 4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4t = 0 + -1
4t = 0 + -1

Combine like terms: 0 + -1 = -1
4t = -1

Divide each side by '4'.
t = -0.25

Simplifying
t = -0.25
Solution
t = {2, -0.25}

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