(5x+9)(9-4x)=0

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


Simplifying
(5x + 9)(9 + -4x) = 0

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

Multiply (9 + 5x) * (9 + -4x)
(9(9 + -4x) + 5x * (9 + -4x)) = 0
((9 * 9 + -4x * 9) + 5x * (9 + -4x)) = 0
((81 + -36x) + 5x * (9 + -4x)) = 0
(81 + -36x + (9 * 5x + -4x * 5x)) = 0
(81 + -36x + (45x + -20x2)) = 0

Combine like terms: -36x + 45x = 9x
(81 + 9x + -20x2) = 0

Solving
81 + 9x + -20x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(9 + 5x)' equal to zero and attempt to solve:

Simplifying
9 + 5x = 0

Solving
9 + 5x = 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 + 5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5x = 0 + -9
5x = 0 + -9

Combine like terms: 0 + -9 = -9
5x = -9

Divide each side by '5'.
x = -1.8

Simplifying
x = -1.8
Solution
x = {2.25, -1.8}

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