(9x-2)(5x+10)=0

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Solution for (9x-2)(5x+10)=0 equation: 


Simplifying
(9x + -2)(5x + 10) = 0

Reorder the terms:
(-2 + 9x)(5x + 10) = 0

Reorder the terms:
(-2 + 9x)(10 + 5x) = 0

Multiply (-2 + 9x) * (10 + 5x)
(-2(10 + 5x) + 9x * (10 + 5x)) = 0
((10 * -2 + 5x * -2) + 9x * (10 + 5x)) = 0
((-20 + -10x) + 9x * (10 + 5x)) = 0
(-20 + -10x + (10 * 9x + 5x * 9x)) = 0
(-20 + -10x + (90x + 45x2)) = 0

Combine like terms: -10x + 90x = 80x
(-20 + 80x + 45x2) = 0

Solving
-20 + 80x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 16x + 9x2) = 0

Factor a trinomial.
5((-2 + -1x)(2 + -9x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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

Simplifying
2 + -9x = 0

Solving
2 + -9x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9x = 0 + -2
-9x = 0 + -2

Combine like terms: 0 + -2 = -2
-9x = -2

Divide each side by '-9'.
x = 0.2222222222

Simplifying
x = 0.2222222222
Solution
x = {-2, 0.2222222222}

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