5(5x+1)(2x+3)=0

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Solution for 5(5x+1)(2x+3)=0 equation: 


Simplifying
5(5x + 1)(2x + 3) = 0

Reorder the terms:
5(1 + 5x)(2x + 3) = 0

Reorder the terms:
5(1 + 5x)(3 + 2x) = 0

Multiply (1 + 5x) * (3 + 2x)
5(1(3 + 2x) + 5x * (3 + 2x)) = 0
5((3 * 1 + 2x * 1) + 5x * (3 + 2x)) = 0
5((3 + 2x) + 5x * (3 + 2x)) = 0
5(3 + 2x + (3 * 5x + 2x * 5x)) = 0
5(3 + 2x + (15x + 10x2)) = 0

Combine like terms: 2x + 15x = 17x
5(3 + 17x + 10x2) = 0
(3 * 5 + 17x * 5 + 10x2 * 5) = 0
(15 + 85x + 50x2) = 0

Solving
15 + 85x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + 17x + 10x2) = 0

Factor a trinomial.
5((3 + 2x)(1 + 5x)) = 0

Ignore the factor 5.

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 '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-1.5, -0.2}

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