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

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


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

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

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

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

Combine like terms: 10x + -15x = -5x
(-50 + -5x + 3x2) = 0

Solving
-50 + -5x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + -3x)(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3.333333333, 5}

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