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

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


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

Reorder the terms:
2x(3 + x) + x(x + 4) = 5x(x + 2) + -2x
(3 * 2x + x * 2x) + x(x + 4) = 5x(x + 2) + -2x
(6x + 2x2) + x(x + 4) = 5x(x + 2) + -2x

Reorder the terms:
6x + 2x2 + x(4 + x) = 5x(x + 2) + -2x
6x + 2x2 + (4 * x + x * x) = 5x(x + 2) + -2x
6x + 2x2 + (4x + x2) = 5x(x + 2) + -2x

Reorder the terms:
6x + 4x + 2x2 + x2 = 5x(x + 2) + -2x

Combine like terms: 6x + 4x = 10x
10x + 2x2 + x2 = 5x(x + 2) + -2x

Combine like terms: 2x2 + x2 = 3x2
10x + 3x2 = 5x(x + 2) + -2x

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

Reorder the terms:
10x + 3x2 = 10x + -2x + 5x2

Combine like terms: 10x + -2x = 8x
10x + 3x2 = 8x + 5x2

Solving
10x + 3x2 = 8x + 5x2

Solving for variable 'x'.

Reorder the terms:
10x + -8x + 3x2 + -5x2 = 8x + 5x2 + -8x + -5x2

Combine like terms: 10x + -8x = 2x
2x + 3x2 + -5x2 = 8x + 5x2 + -8x + -5x2

Combine like terms: 3x2 + -5x2 = -2x2
2x + -2x2 = 8x + 5x2 + -8x + -5x2

Reorder the terms:
2x + -2x2 = 8x + -8x + 5x2 + -5x2

Combine like terms: 8x + -8x = 0
2x + -2x2 = 0 + 5x2 + -5x2
2x + -2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -1x) = 0

Ignore the factor 2.

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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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