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

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


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

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

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

Multiply (6 + 4x) * (5 + 6x)
(6(5 + 6x) + 4x * (5 + 6x)) = 0
((5 * 6 + 6x * 6) + 4x * (5 + 6x)) = 0
((30 + 36x) + 4x * (5 + 6x)) = 0
(30 + 36x + (5 * 4x + 6x * 4x)) = 0
(30 + 36x + (20x + 24x2)) = 0

Combine like terms: 36x + 20x = 56x
(30 + 56x + 24x2) = 0

Solving
30 + 56x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 28x + 12x2) = 0

Factor a trinomial.
2((3 + 2x)(5 + 6x)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {-1.5, -0.8333333333}

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