(4x-9)(8-x)=0

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Solution for (4x-9)(8-x)=0 equation: 


Simplifying
(4x + -9)(8 + -1x) = 0

Reorder the terms:
(-9 + 4x)(8 + -1x) = 0

Multiply (-9 + 4x) * (8 + -1x)
(-9(8 + -1x) + 4x * (8 + -1x)) = 0
((8 * -9 + -1x * -9) + 4x * (8 + -1x)) = 0
((-72 + 9x) + 4x * (8 + -1x)) = 0
(-72 + 9x + (8 * 4x + -1x * 4x)) = 0
(-72 + 9x + (32x + -4x2)) = 0

Combine like terms: 9x + 32x = 41x
(-72 + 41x + -4x2) = 0

Solving
-72 + 41x + -4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + x)(9 + -4x) = 0


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

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

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

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

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

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {8, 2.25}

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