2x(x+1)=5x(x-7)

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Solution for 2x(x+1)=5x(x-7) equation: 


Simplifying
2x(x + 1) = 5x(x + -7)

Reorder the terms:
2x(1 + x) = 5x(x + -7)
(1 * 2x + x * 2x) = 5x(x + -7)
(2x + 2x2) = 5x(x + -7)

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

Solving
2x + 2x2 = -35x + 5x2

Solving for variable 'x'.

Reorder the terms:
2x + 35x + 2x2 + -5x2 = -35x + 5x2 + 35x + -5x2

Combine like terms: 2x + 35x = 37x
37x + 2x2 + -5x2 = -35x + 5x2 + 35x + -5x2

Combine like terms: 2x2 + -5x2 = -3x2
37x + -3x2 = -35x + 5x2 + 35x + -5x2

Reorder the terms:
37x + -3x2 = -35x + 35x + 5x2 + -5x2

Combine like terms: -35x + 35x = 0
37x + -3x2 = 0 + 5x2 + -5x2
37x + -3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
37x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(37 + -3x) = 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 '(37 + -3x)' equal to zero and attempt to solve:

Simplifying
37 + -3x = 0

Solving
37 + -3x = 0

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

Add '-37' to each side of the equation.
37 + -37 + -3x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -3x = 0 + -37
-3x = 0 + -37

Combine like terms: 0 + -37 = -37
-3x = -37

Divide each side by '-3'.
x = 12.33333333

Simplifying
x = 12.33333333
Solution
x = {0, 12.33333333}

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