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

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


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

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

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

Multiply (5 + 2t) * (-7 + t)
4t(5(-7 + t) + 2t * (-7 + t)) = 0
4t((-7 * 5 + t * 5) + 2t * (-7 + t)) = 0
4t((-35 + 5t) + 2t * (-7 + t)) = 0
4t(-35 + 5t + (-7 * 2t + t * 2t)) = 0
4t(-35 + 5t + (-14t + 2t2)) = 0

Combine like terms: 5t + -14t = -9t
4t(-35 + -9t + 2t2) = 0
(-35 * 4t + -9t * 4t + 2t2 * 4t) = 0
(-140t + -36t2 + 8t3) = 0

Solving
-140t + -36t2 + 8t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4t'.
4t(-35 + -9t + 2t2) = 0

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

Ignore the factor 4.

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 '(-5 + -2t)' equal to zero and attempt to solve:

Simplifying
-5 + -2t = 0

Solving
-5 + -2t = 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 + -2t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2t = 0 + 5
-2t = 0 + 5

Combine like terms: 0 + 5 = 5
-2t = 5

Divide each side by '-2'.
t = -2.5

Simplifying
t = -2.5

Subproblem 3
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 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 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {0, -2.5, 7}

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