(3t-2)x(4t+5)=

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Solution for (3t-2)x(4t+5)= equation: 


Simplifying
(3t + -2) * x(4t + 5) = 0

Reorder the terms:
(-2 + 3t) * x(4t + 5) = 0

Reorder the terms:
(-2 + 3t) * x(5 + 4t) = 0

Reorder the terms for easier multiplication:
x(-2 + 3t)(5 + 4t) = 0

Multiply (-2 + 3t) * (5 + 4t)
x(-2(5 + 4t) + 3t * (5 + 4t)) = 0
x((5 * -2 + 4t * -2) + 3t * (5 + 4t)) = 0
x((-10 + -8t) + 3t * (5 + 4t)) = 0
x(-10 + -8t + (5 * 3t + 4t * 3t)) = 0
x(-10 + -8t + (15t + 12t2)) = 0

Combine like terms: -8t + 15t = 7t
x(-10 + 7t + 12t2) = 0
(-10 * x + 7t * x + 12t2 * x) = 0

Reorder the terms:
(7tx + 12t2x + -10x) = 0
(7tx + 12t2x + -10x) = 0

Solving
7tx + 12t2x + -10x = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7t + 12t2 + -10) = 0

Factor a trinomial.
x((3t + -2)(4t + 5)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3t + -2)' equal to zero and attempt to solve:

Simplifying
3t + -2 = 0

Reorder the terms:
-2 + 3t = 0

Solving
-2 + 3t = 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 + 3t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3t = 0 + 2
3t = 0 + 2

Combine like terms: 0 + 2 = 2
3t = 2

Divide each side by '3'.
t = 0.6666666667

Simplifying
t = 0.6666666667

Subproblem 3
Set the factor '(4t + 5)' equal to zero and attempt to solve:

Simplifying
4t + 5 = 0

Reorder the terms:
5 + 4t = 0

Solving
5 + 4t = 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 + 4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4t = 0 + -5
4t = 0 + -5

Combine like terms: 0 + -5 = -5
4t = -5

Divide each side by '4'.
t = -1.25

Simplifying
t = -1.25
Solution
t = {0.6666666667, -1.25}

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