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

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


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

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

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

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

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

Solving
-81 + -36x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-9 + -4x + 5x2) = 0

Factor a trinomial.
9((-1 + -1x)(9 + -5x)) = 0

Ignore the factor 9.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1

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 = {-1, 1.8}

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