11(x^2+2x)=2x(5x+8)

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Solution for 11(x^2+2x)=2x(5x+8) equation: 


Simplifying
11(x2 + 2x) = 2x(5x + 8)

Reorder the terms:
11(2x + x2) = 2x(5x + 8)
(2x * 11 + x2 * 11) = 2x(5x + 8)
(22x + 11x2) = 2x(5x + 8)

Reorder the terms:
22x + 11x2 = 2x(8 + 5x)
22x + 11x2 = (8 * 2x + 5x * 2x)
22x + 11x2 = (16x + 10x2)

Solving
22x + 11x2 = 16x + 10x2

Solving for variable 'x'.

Reorder the terms:
22x + -16x + 11x2 + -10x2 = 16x + 10x2 + -16x + -10x2

Combine like terms: 22x + -16x = 6x
6x + 11x2 + -10x2 = 16x + 10x2 + -16x + -10x2

Combine like terms: 11x2 + -10x2 = 1x2
6x + 1x2 = 16x + 10x2 + -16x + -10x2

Reorder the terms:
6x + 1x2 = 16x + -16x + 10x2 + -10x2

Combine like terms: 16x + -16x = 0
6x + 1x2 = 0 + 10x2 + -10x2
6x + 1x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
6x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {0, -6}

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