5x(3x+20)=x(2x+3)

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Solution for 5x(3x+20)=x(2x+3) equation: 


Simplifying
5x(3x + 20) = x(2x + 3)

Reorder the terms:
5x(20 + 3x) = x(2x + 3)
(20 * 5x + 3x * 5x) = x(2x + 3)
(100x + 15x2) = x(2x + 3)

Reorder the terms:
100x + 15x2 = x(3 + 2x)
100x + 15x2 = (3 * x + 2x * x)
100x + 15x2 = (3x + 2x2)

Solving
100x + 15x2 = 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
100x + -3x + 15x2 + -2x2 = 3x + 2x2 + -3x + -2x2

Combine like terms: 100x + -3x = 97x
97x + 15x2 + -2x2 = 3x + 2x2 + -3x + -2x2

Combine like terms: 15x2 + -2x2 = 13x2
97x + 13x2 = 3x + 2x2 + -3x + -2x2

Reorder the terms:
97x + 13x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
97x + 13x2 = 0 + 2x2 + -2x2
97x + 13x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
97x + 13x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(97 + 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 '(97 + 13x)' equal to zero and attempt to solve:

Simplifying
97 + 13x = 0

Solving
97 + 13x = 0

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

Add '-97' to each side of the equation.
97 + -97 + 13x = 0 + -97

Combine like terms: 97 + -97 = 0
0 + 13x = 0 + -97
13x = 0 + -97

Combine like terms: 0 + -97 = -97
13x = -97

Divide each side by '13'.
x = -7.461538462

Simplifying
x = -7.461538462
Solution
x = {0, -7.461538462}

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