3t(t-5)(4t+7)=0

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Solution for 3t(t-5)(4t+7)=0 equation: 


Simplifying
3t(t + -5)(4t + 7) = 0

Reorder the terms:
3t(-5 + t)(4t + 7) = 0

Reorder the terms:
3t(-5 + t)(7 + 4t) = 0

Multiply (-5 + t) * (7 + 4t)
3t(-5(7 + 4t) + t(7 + 4t)) = 0
3t((7 * -5 + 4t * -5) + t(7 + 4t)) = 0
3t((-35 + -20t) + t(7 + 4t)) = 0
3t(-35 + -20t + (7 * t + 4t * t)) = 0
3t(-35 + -20t + (7t + 4t2)) = 0

Combine like terms: -20t + 7t = -13t
3t(-35 + -13t + 4t2) = 0
(-35 * 3t + -13t * 3t + 4t2 * 3t) = 0
(-105t + -39t2 + 12t3) = 0

Solving
-105t + -39t2 + 12t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3t'.
3t(-35 + -13t + 4t2) = 0

Factor a trinomial.
3t((-7 + -4t)(5 + -1t)) = 0

Ignore the factor 3.

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 '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {0, -1.75, 5}

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