(4x+10)(3x+9)=0

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Solution for (4x+10)(3x+9)=0 equation: 


Simplifying
(4x + 10)(3x + 9) = 0

Reorder the terms:
(10 + 4x)(3x + 9) = 0

Reorder the terms:
(10 + 4x)(9 + 3x) = 0

Multiply (10 + 4x) * (9 + 3x)
(10(9 + 3x) + 4x * (9 + 3x)) = 0
((9 * 10 + 3x * 10) + 4x * (9 + 3x)) = 0
((90 + 30x) + 4x * (9 + 3x)) = 0
(90 + 30x + (9 * 4x + 3x * 4x)) = 0
(90 + 30x + (36x + 12x2)) = 0

Combine like terms: 30x + 36x = 66x
(90 + 66x + 12x2) = 0

Solving
90 + 66x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(15 + 11x + 2x2) = 0

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

Ignore the factor 6.

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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {-3, -2.5}

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