(4t)(6t^2-5)(7t^2-2)=

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Solution for (4t)(6t^2-5)(7t^2-2)= equation: 


Simplifying
(4t)(6t2 + -5)(7t2 + -2) = 0

Remove parenthesis around (4t)
4t(6t2 + -5)(7t2 + -2) = 0

Reorder the terms:
4t(-5 + 6t2)(7t2 + -2) = 0

Reorder the terms:
4t(-5 + 6t2)(-2 + 7t2) = 0

Multiply (-5 + 6t2) * (-2 + 7t2)
4t(-5(-2 + 7t2) + 6t2 * (-2 + 7t2)) = 0
4t((-2 * -5 + 7t2 * -5) + 6t2 * (-2 + 7t2)) = 0
4t((10 + -35t2) + 6t2 * (-2 + 7t2)) = 0
4t(10 + -35t2 + (-2 * 6t2 + 7t2 * 6t2)) = 0
4t(10 + -35t2 + (-12t2 + 42t4)) = 0

Combine like terms: -35t2 + -12t2 = -47t2
4t(10 + -47t2 + 42t4) = 0
(10 * 4t + -47t2 * 4t + 42t4 * 4t) = 0
(40t + -188t3 + 168t5) = 0

Solving
40t + -188t3 + 168t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4t'.
4t(10 + -47t2 + 42t4) = 0

Factor a trinomial.
4t((2 + -7t2)(5 + -6t2)) = 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 '(2 + -7t2)' equal to zero and attempt to solve:

Simplifying
2 + -7t2 = 0

Solving
2 + -7t2 = 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 + -7t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7t2 = 0 + -2
-7t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7t2 = -2

Divide each side by '-7'.
t2 = 0.2857142857

Simplifying
t2 = 0.2857142857

Take the square root of each side:
t = {-0.534522484, 0.534522484}

Subproblem 3
Set the factor '(5 + -6t2)' equal to zero and attempt to solve:

Simplifying
5 + -6t2 = 0

Solving
5 + -6t2 = 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 + -6t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6t2 = 0 + -5
-6t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-6t2 = -5

Divide each side by '-6'.
t2 = 0.8333333333

Simplifying
t2 = 0.8333333333

Take the square root of each side:
t = {-0.912870929, 0.912870929}
Solution
t = {0, -0.534522484, 0.534522484, -0.912870929, 0.912870929}

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