4x(x+2)+4x(3x+5)=0

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Solution for 4x(x+2)+4x(3x+5)=0 equation: 


Simplifying
4x(x + 2) + 4x(3x + 5) = 0

Reorder the terms:
4x(2 + x) + 4x(3x + 5) = 0
(2 * 4x + x * 4x) + 4x(3x + 5) = 0
(8x + 4x2) + 4x(3x + 5) = 0

Reorder the terms:
8x + 4x2 + 4x(5 + 3x) = 0
8x + 4x2 + (5 * 4x + 3x * 4x) = 0
8x + 4x2 + (20x + 12x2) = 0

Reorder the terms:
8x + 20x + 4x2 + 12x2 = 0

Combine like terms: 8x + 20x = 28x
28x + 4x2 + 12x2 = 0

Combine like terms: 4x2 + 12x2 = 16x2
28x + 16x2 = 0

Solving
28x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(7 + 4x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {0, -1.75}

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