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

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


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

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

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

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

Combine like terms: -45x + 20x = -25x
(-20 + -25x + 45x2) = 0

Solving
-20 + -25x + 45x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
5((-4 + -9x)(1 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + -9x)' equal to zero and attempt to solve:

Simplifying
-4 + -9x = 0

Solving
-4 + -9x = 0

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

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

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

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

Divide each side by '-9'.
x = -0.4444444444

Simplifying
x = -0.4444444444

Subproblem 2
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
Solution
x = {-0.4444444444, 1}

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