(6x+5)(4x+12)=0

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Solution for (6x+5)(4x+12)=0 equation: 


Simplifying
(6x + 5)(4x + 12) = 0

Reorder the terms:
(5 + 6x)(4x + 12) = 0

Reorder the terms:
(5 + 6x)(12 + 4x) = 0

Multiply (5 + 6x) * (12 + 4x)
(5(12 + 4x) + 6x * (12 + 4x)) = 0
((12 * 5 + 4x * 5) + 6x * (12 + 4x)) = 0
((60 + 20x) + 6x * (12 + 4x)) = 0
(60 + 20x + (12 * 6x + 4x * 6x)) = 0
(60 + 20x + (72x + 24x2)) = 0

Combine like terms: 20x + 72x = 92x
(60 + 92x + 24x2) = 0

Solving
60 + 92x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + 23x + 6x2) = 0

Factor a trinomial.
4((3 + x)(5 + 6x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 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 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {-3, -0.8333333333}

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