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

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


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

Multiply (2s + -5t) * (4s + 9t)
(2s * (4s + 9t) + -5t * (4s + 9t)) = 0
((4s * 2s + 9t * 2s) + -5t * (4s + 9t)) = 0

Reorder the terms:
((18st + 8s2) + -5t * (4s + 9t)) = 0
((18st + 8s2) + -5t * (4s + 9t)) = 0
(18st + 8s2 + (4s * -5t + 9t * -5t)) = 0
(18st + 8s2 + (-20st + -45t2)) = 0

Reorder the terms:
(18st + -20st + 8s2 + -45t2) = 0

Combine like terms: 18st + -20st = -2st
(-2st + 8s2 + -45t2) = 0

Solving
-2st + 8s2 + -45t2 = 0

Solving for variable 's'.

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


Subproblem 1
Set the factor '(2s + -5t)' equal to zero and attempt to solve:

Simplifying
2s + -5t = 0

Solving
2s + -5t = 0

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

Add '5t' to each side of the equation.
2s + -5t + 5t = 0 + 5t

Combine like terms: -5t + 5t = 0
2s + 0 = 0 + 5t
2s = 0 + 5t
Remove the zero:
2s = 5t

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

Simplifying
s = 2.5t

Subproblem 2
Set the factor '(4s + 9t)' equal to zero and attempt to solve:

Simplifying
4s + 9t = 0

Solving
4s + 9t = 0

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

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

Combine like terms: 9t + -9t = 0
4s + 0 = 0 + -9t
4s = 0 + -9t
Remove the zero:
4s = -9t

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

Simplifying
s = -2.25t
Solution
s = {2.5t, -2.25t}

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