5(6x+3)(2x+5)=0

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Solution for 5(6x+3)(2x+5)=0 equation: 


Simplifying
5(6x + 3)(2x + 5) = 0

Reorder the terms:
5(3 + 6x)(2x + 5) = 0

Reorder the terms:
5(3 + 6x)(5 + 2x) = 0

Multiply (3 + 6x) * (5 + 2x)
5(3(5 + 2x) + 6x * (5 + 2x)) = 0
5((5 * 3 + 2x * 3) + 6x * (5 + 2x)) = 0
5((15 + 6x) + 6x * (5 + 2x)) = 0
5(15 + 6x + (5 * 6x + 2x * 6x)) = 0
5(15 + 6x + (30x + 12x2)) = 0

Combine like terms: 6x + 30x = 36x
5(15 + 36x + 12x2) = 0
(15 * 5 + 36x * 5 + 12x2 * 5) = 0
(75 + 180x + 60x2) = 0

Solving
75 + 180x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(5 + 12x + 4x2) = 0

Factor a trinomial.
15((5 + 2x)(1 + 2x)) = 0

Ignore the factor 15.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2.5, -0.5}

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