5t(4t+7)(t-2)=

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Solution for 5t(4t+7)(t-2)= equation: 


Simplifying
5t(4t + 7)(t + -2) = 0

Reorder the terms:
5t(7 + 4t)(t + -2) = 0

Reorder the terms:
5t(7 + 4t)(-2 + t) = 0

Multiply (7 + 4t) * (-2 + t)
5t(7(-2 + t) + 4t * (-2 + t)) = 0
5t((-2 * 7 + t * 7) + 4t * (-2 + t)) = 0
5t((-14 + 7t) + 4t * (-2 + t)) = 0
5t(-14 + 7t + (-2 * 4t + t * 4t)) = 0
5t(-14 + 7t + (-8t + 4t2)) = 0

Combine like terms: 7t + -8t = -1t
5t(-14 + -1t + 4t2) = 0
(-14 * 5t + -1t * 5t + 4t2 * 5t) = 0
(-70t + -5t2 + 20t3) = 0

Solving
-70t + -5t2 + 20t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5t'.
5t(-14 + -1t + 4t2) = 0

Factor a trinomial.
5t((-7 + -4t)(2 + -1t)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

Subproblem 2
Set the factor '(-7 + -4t)' equal to zero and attempt to solve:

Simplifying
-7 + -4t = 0

Solving
-7 + -4t = 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 + -4t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4t = 0 + 7
-4t = 0 + 7

Combine like terms: 0 + 7 = 7
-4t = 7

Divide each side by '-4'.
t = -1.75

Simplifying
t = -1.75

Subproblem 3
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 = {0, -1.75, 2}

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