(3x+1)(2x+10)=0

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Solution for (3x+1)(2x+10)=0 equation: 


Simplifying
(3x + 1)(2x + 10) = 0

Reorder the terms:
(1 + 3x)(2x + 10) = 0

Reorder the terms:
(1 + 3x)(10 + 2x) = 0

Multiply (1 + 3x) * (10 + 2x)
(1(10 + 2x) + 3x * (10 + 2x)) = 0
((10 * 1 + 2x * 1) + 3x * (10 + 2x)) = 0
((10 + 2x) + 3x * (10 + 2x)) = 0
(10 + 2x + (10 * 3x + 2x * 3x)) = 0
(10 + 2x + (30x + 6x2)) = 0

Combine like terms: 2x + 30x = 32x
(10 + 32x + 6x2) = 0

Solving
10 + 32x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 16x + 3x2) = 0

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

Ignore the factor 2.

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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-5, -0.3333333333}

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