(4x+6)(3x+5)=0

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Solution for (4x+6)(3x+5)=0 equation: 


Simplifying
(4x + 6)(3x + 5) = 0

Reorder the terms:
(6 + 4x)(3x + 5) = 0

Reorder the terms:
(6 + 4x)(5 + 3x) = 0

Multiply (6 + 4x) * (5 + 3x)
(6(5 + 3x) + 4x * (5 + 3x)) = 0
((5 * 6 + 3x * 6) + 4x * (5 + 3x)) = 0
((30 + 18x) + 4x * (5 + 3x)) = 0
(30 + 18x + (5 * 4x + 3x * 4x)) = 0
(30 + 18x + (20x + 12x2)) = 0

Combine like terms: 18x + 20x = 38x
(30 + 38x + 12x2) = 0

Solving
30 + 38x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 19x + 6x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, -1.5}

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