2x(3x+13)=x(5x-20)

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Solution for 2x(3x+13)=x(5x-20) equation: 


Simplifying
2x(3x + 13) = x(5x + -20)

Reorder the terms:
2x(13 + 3x) = x(5x + -20)
(13 * 2x + 3x * 2x) = x(5x + -20)
(26x + 6x2) = x(5x + -20)

Reorder the terms:
26x + 6x2 = x(-20 + 5x)
26x + 6x2 = (-20 * x + 5x * x)
26x + 6x2 = (-20x + 5x2)

Solving
26x + 6x2 = -20x + 5x2

Solving for variable 'x'.

Reorder the terms:
26x + 20x + 6x2 + -5x2 = -20x + 5x2 + 20x + -5x2

Combine like terms: 26x + 20x = 46x
46x + 6x2 + -5x2 = -20x + 5x2 + 20x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
46x + 1x2 = -20x + 5x2 + 20x + -5x2

Reorder the terms:
46x + 1x2 = -20x + 20x + 5x2 + -5x2

Combine like terms: -20x + 20x = 0
46x + 1x2 = 0 + 5x2 + -5x2
46x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
46x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(46 + x) = 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 '(46 + x)' equal to zero and attempt to solve:

Simplifying
46 + x = 0

Solving
46 + x = 0

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

Add '-46' to each side of the equation.
46 + -46 + x = 0 + -46

Combine like terms: 46 + -46 = 0
0 + x = 0 + -46
x = 0 + -46

Combine like terms: 0 + -46 = -46
x = -46

Simplifying
x = -46
Solution
x = {0, -46}

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