x(x+3)-5(2x-4)=2x

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Solution for x(x+3)-5(2x-4)=2x equation: 


Simplifying
x(x + 3) + -5(2x + -4) = 2x

Reorder the terms:
x(3 + x) + -5(2x + -4) = 2x
(3 * x + x * x) + -5(2x + -4) = 2x
(3x + x2) + -5(2x + -4) = 2x

Reorder the terms:
3x + x2 + -5(-4 + 2x) = 2x
3x + x2 + (-4 * -5 + 2x * -5) = 2x
3x + x2 + (20 + -10x) = 2x

Reorder the terms:
20 + 3x + -10x + x2 = 2x

Combine like terms: 3x + -10x = -7x
20 + -7x + x2 = 2x

Solving
20 + -7x + x2 = 2x

Solving for variable 'x'.

Reorder the terms:
20 + -7x + -2x + x2 = 2x + -2x

Combine like terms: -7x + -2x = -9x
20 + -9x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
20 + -9x + x2 = 0

Factor a trinomial.
(4 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {4, 5}

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