(5t-2)(4t+9)=0

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Solution for (5t-2)(4t+9)=0 equation: 


Simplifying
(5t + -2)(4t + 9) = 0

Reorder the terms:
(-2 + 5t)(4t + 9) = 0

Reorder the terms:
(-2 + 5t)(9 + 4t) = 0

Multiply (-2 + 5t) * (9 + 4t)
(-2(9 + 4t) + 5t * (9 + 4t)) = 0
((9 * -2 + 4t * -2) + 5t * (9 + 4t)) = 0
((-18 + -8t) + 5t * (9 + 4t)) = 0
(-18 + -8t + (9 * 5t + 4t * 5t)) = 0
(-18 + -8t + (45t + 20t2)) = 0

Combine like terms: -8t + 45t = 37t
(-18 + 37t + 20t2) = 0

Solving
-18 + 37t + 20t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-9 + -4t)(2 + -5t) = 0


Subproblem 1
Set the factor '(-9 + -4t)' equal to zero and attempt to solve:

Simplifying
-9 + -4t = 0

Solving
-9 + -4t = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4t = 0 + 9
-4t = 0 + 9

Combine like terms: 0 + 9 = 9
-4t = 9

Divide each side by '-4'.
t = -2.25

Simplifying
t = -2.25

Subproblem 2
Set the factor '(2 + -5t)' equal to zero and attempt to solve:

Simplifying
2 + -5t = 0

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

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

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

Divide each side by '-5'.
t = 0.4

Simplifying
t = 0.4
Solution
t = {-2.25, 0.4}

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