(8x+4)(5x+10)=0

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Solution for (8x+4)(5x+10)=0 equation: 


Simplifying
(8x + 4)(5x + 10) = 0

Reorder the terms:
(4 + 8x)(5x + 10) = 0

Reorder the terms:
(4 + 8x)(10 + 5x) = 0

Multiply (4 + 8x) * (10 + 5x)
(4(10 + 5x) + 8x * (10 + 5x)) = 0
((10 * 4 + 5x * 4) + 8x * (10 + 5x)) = 0
((40 + 20x) + 8x * (10 + 5x)) = 0
(40 + 20x + (10 * 8x + 5x * 8x)) = 0
(40 + 20x + (80x + 40x2)) = 0

Combine like terms: 20x + 80x = 100x
(40 + 100x + 40x2) = 0

Solving
40 + 100x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(2 + 5x + 2x2) = 0

Factor a trinomial.
20((2 + x)(1 + 2x)) = 0

Ignore the factor 20.

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 '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2, -0.5}

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