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

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


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

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

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

Multiply (10 + 5x) * (10 + 9x)
(10(10 + 9x) + 5x * (10 + 9x)) = 0
((10 * 10 + 9x * 10) + 5x * (10 + 9x)) = 0
((100 + 90x) + 5x * (10 + 9x)) = 0
(100 + 90x + (10 * 5x + 9x * 5x)) = 0
(100 + 90x + (50x + 45x2)) = 0

Combine like terms: 90x + 50x = 140x
(100 + 140x + 45x2) = 0

Solving
100 + 140x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + 28x + 9x2) = 0

Factor a trinomial.
5((2 + x)(10 + 9x)) = 0

Ignore the factor 5.

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(10 + 9x)' equal to zero and attempt to solve:

Simplifying
10 + 9x = 0

Solving
10 + 9x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 9x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9x = 0 + -10
9x = 0 + -10

Combine like terms: 0 + -10 = -10
9x = -10

Divide each side by '9'.
x = -1.111111111

Simplifying
x = -1.111111111
Solution
x = {-2, -1.111111111}

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