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

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


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

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

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

Multiply (8 + 2x) * (4 + 3x)
(8(4 + 3x) + 2x * (4 + 3x)) = 0
((4 * 8 + 3x * 8) + 2x * (4 + 3x)) = 0
((32 + 24x) + 2x * (4 + 3x)) = 0
(32 + 24x + (4 * 2x + 3x * 2x)) = 0
(32 + 24x + (8x + 6x2)) = 0

Combine like terms: 24x + 8x = 32x
(32 + 32x + 6x2) = 0

Solving
32 + 32x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 16x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-4, -1.333333333}

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