(5x+3)(3x+10)=0

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Solution for (5x+3)(3x+10)=0 equation: 


Simplifying
(5x + 3)(3x + 10) = 0

Reorder the terms:
(3 + 5x)(3x + 10) = 0

Reorder the terms:
(3 + 5x)(10 + 3x) = 0

Multiply (3 + 5x) * (10 + 3x)
(3(10 + 3x) + 5x * (10 + 3x)) = 0
((10 * 3 + 3x * 3) + 5x * (10 + 3x)) = 0
((30 + 9x) + 5x * (10 + 3x)) = 0
(30 + 9x + (10 * 5x + 3x * 5x)) = 0
(30 + 9x + (50x + 15x2)) = 0

Combine like terms: 9x + 50x = 59x
(30 + 59x + 15x2) = 0

Solving
30 + 59x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + 3x)(3 + 5x) = 0


Subproblem 1
Set the factor '(10 + 3x)' equal to zero and attempt to solve:

Simplifying
10 + 3x = 0

Solving
10 + 3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x = 0 + -10
3x = 0 + -10

Combine like terms: 0 + -10 = -10
3x = -10

Divide each side by '3'.
x = -3.333333333

Simplifying
x = -3.333333333

Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

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

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

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

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6
Solution
x = {-3.333333333, -0.6}

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