(x+ut)(9x-8ut)=

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Solution for (x+ut)(9x-8ut)= equation: 


Simplifying
(x + ut)(9x + -8ut) = 0

Reorder the terms:
(tu + x)(9x + -8ut) = 0

Reorder the terms:
(tu + x)(-8tu + 9x) = 0

Multiply (tu + x) * (-8tu + 9x)
(tu(-8tu + 9x) + x(-8tu + 9x)) = 0
((-8tu * tu + 9x * tu) + x(-8tu + 9x)) = 0

Reorder the terms:
((9tux + -8t2u2) + x(-8tu + 9x)) = 0
((9tux + -8t2u2) + x(-8tu + 9x)) = 0
(9tux + -8t2u2 + (-8tu * x + 9x * x)) = 0
(9tux + -8t2u2 + (-8tux + 9x2)) = 0

Reorder the terms:
(9tux + -8tux + -8t2u2 + 9x2) = 0

Combine like terms: 9tux + -8tux = 1tux
(1tux + -8t2u2 + 9x2) = 0

Solving
1tux + -8t2u2 + 9x2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1tu + -1x)(8tu + -9x) = 0


Subproblem 1
Set the factor '(-1tu + -1x)' equal to zero and attempt to solve:

Simplifying
-1tu + -1x = 0

Solving
-1tu + -1x = 0

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

Add 'x' to each side of the equation.
-1tu + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-1tu + 0 = 0 + x
-1tu = 0 + x
Remove the zero:
-1tu = x

Divide each side by '-1u'.
t = -1u-1x

Simplifying
t = -1u-1x

Subproblem 2
Set the factor '(8tu + -9x)' equal to zero and attempt to solve:

Simplifying
8tu + -9x = 0

Solving
8tu + -9x = 0

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

Add '9x' to each side of the equation.
8tu + -9x + 9x = 0 + 9x

Combine like terms: -9x + 9x = 0
8tu + 0 = 0 + 9x
8tu = 0 + 9x
Remove the zero:
8tu = 9x

Divide each side by '8u'.
t = 1.125u-1x

Simplifying
t = 1.125u-1x
Solution
t = {-1u-1x, 1.125u-1x}

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