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

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


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

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

Remove parenthesis around (5x)
(-2 + x) * 5x = x(x + 1)

Reorder the terms for easier multiplication:
5x(-2 + x) = x(x + 1)
(-2 * 5x + x * 5x) = x(x + 1)
(-10x + 5x2) = x(x + 1)

Reorder the terms:
-10x + 5x2 = x(1 + x)
-10x + 5x2 = (1 * x + x * x)
-10x + 5x2 = (1x + x2)

Solving
-10x + 5x2 = 1x + x2

Solving for variable 'x'.

Reorder the terms:
-10x + -1x + 5x2 + -1x2 = 1x + x2 + -1x + -1x2

Combine like terms: -10x + -1x = -11x
-11x + 5x2 + -1x2 = 1x + x2 + -1x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
-11x + 4x2 = 1x + x2 + -1x + -1x2

Reorder the terms:
-11x + 4x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
-11x + 4x2 = 0 + x2 + -1x2
-11x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-11 + 4x) = 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 '(-11 + 4x)' equal to zero and attempt to solve:

Simplifying
-11 + 4x = 0

Solving
-11 + 4x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 4x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4x = 0 + 11
4x = 0 + 11

Combine like terms: 0 + 11 = 11
4x = 11

Divide each side by '4'.
x = 2.75

Simplifying
x = 2.75
Solution
x = {0, 2.75}

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