(2x+4)(4x+10)=0

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Solution for (2x+4)(4x+10)=0 equation: 


Simplifying
(2x + 4)(4x + 10) = 0

Reorder the terms:
(4 + 2x)(4x + 10) = 0

Reorder the terms:
(4 + 2x)(10 + 4x) = 0

Multiply (4 + 2x) * (10 + 4x)
(4(10 + 4x) + 2x * (10 + 4x)) = 0
((10 * 4 + 4x * 4) + 2x * (10 + 4x)) = 0
((40 + 16x) + 2x * (10 + 4x)) = 0
(40 + 16x + (10 * 2x + 4x * 2x)) = 0
(40 + 16x + (20x + 8x2)) = 0

Combine like terms: 16x + 20x = 36x
(40 + 36x + 8x2) = 0

Solving
40 + 36x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + 9x + 2x2) = 0

Factor a trinomial.
4((5 + 2x)(2 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

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

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

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
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
Solution
x = {-2.5, -2}

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