5x(2x+7)+x(3x-5)=0

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Solution for 5x(2x+7)+x(3x-5)=0 equation: 


Simplifying
5x(2x + 7) + x(3x + -5) = 0

Reorder the terms:
5x(7 + 2x) + x(3x + -5) = 0
(7 * 5x + 2x * 5x) + x(3x + -5) = 0
(35x + 10x2) + x(3x + -5) = 0

Reorder the terms:
35x + 10x2 + x(-5 + 3x) = 0
35x + 10x2 + (-5 * x + 3x * x) = 0
35x + 10x2 + (-5x + 3x2) = 0

Reorder the terms:
35x + -5x + 10x2 + 3x2 = 0

Combine like terms: 35x + -5x = 30x
30x + 10x2 + 3x2 = 0

Combine like terms: 10x2 + 3x2 = 13x2
30x + 13x2 = 0

Solving
30x + 13x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(30 + 13x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(30 + 13x)' equal to zero and attempt to solve:

Simplifying
30 + 13x = 0

Solving
30 + 13x = 0

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

Add '-30' to each side of the equation.
30 + -30 + 13x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 13x = 0 + -30
13x = 0 + -30

Combine like terms: 0 + -30 = -30
13x = -30

Divide each side by '13'.
x = -2.307692308

Simplifying
x = -2.307692308
Solution
x = {0, -2.307692308}

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