(4x+8)(2x+3)=0

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Solution for (4x+8)(2x+3)=0 equation: 


Simplifying
(4x + 8)(2x + 3) = 0

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

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

Multiply (8 + 4x) * (3 + 2x)
(8(3 + 2x) + 4x * (3 + 2x)) = 0
((3 * 8 + 2x * 8) + 4x * (3 + 2x)) = 0
((24 + 16x) + 4x * (3 + 2x)) = 0
(24 + 16x + (3 * 4x + 2x * 4x)) = 0
(24 + 16x + (12x + 8x2)) = 0

Combine like terms: 16x + 12x = 28x
(24 + 28x + 8x2) = 0

Solving
24 + 28x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 7x + 2x2) = 0

Factor a trinomial.
4((2 + x)(3 + 2x)) = 0

Ignore the factor 4.

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 '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-2, -1.5}

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