(2x+4)(5x+2)=0

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Solution for (2x+4)(5x+2)=0 equation: 


Simplifying
(2x + 4)(5x + 2) = 0

Reorder the terms:
(4 + 2x)(5x + 2) = 0

Reorder the terms:
(4 + 2x)(2 + 5x) = 0

Multiply (4 + 2x) * (2 + 5x)
(4(2 + 5x) + 2x * (2 + 5x)) = 0
((2 * 4 + 5x * 4) + 2x * (2 + 5x)) = 0
((8 + 20x) + 2x * (2 + 5x)) = 0
(8 + 20x + (2 * 2x + 5x * 2x)) = 0
(8 + 20x + (4x + 10x2)) = 0

Combine like terms: 20x + 4x = 24x
(8 + 24x + 10x2) = 0

Solving
8 + 24x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 12x + 5x2) = 0

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

Ignore the factor 2.

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 '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 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 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {-2, -0.4}

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