2x(5x+23)=x(11x+27)

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Solution for 2x(5x+23)=x(11x+27) equation: 


Simplifying
2x(5x + 23) = x(11x + 27)

Reorder the terms:
2x(23 + 5x) = x(11x + 27)
(23 * 2x + 5x * 2x) = x(11x + 27)
(46x + 10x2) = x(11x + 27)

Reorder the terms:
46x + 10x2 = x(27 + 11x)
46x + 10x2 = (27 * x + 11x * x)
46x + 10x2 = (27x + 11x2)

Solving
46x + 10x2 = 27x + 11x2

Solving for variable 'x'.

Reorder the terms:
46x + -27x + 10x2 + -11x2 = 27x + 11x2 + -27x + -11x2

Combine like terms: 46x + -27x = 19x
19x + 10x2 + -11x2 = 27x + 11x2 + -27x + -11x2

Combine like terms: 10x2 + -11x2 = -1x2
19x + -1x2 = 27x + 11x2 + -27x + -11x2

Reorder the terms:
19x + -1x2 = 27x + -27x + 11x2 + -11x2

Combine like terms: 27x + -27x = 0
19x + -1x2 = 0 + 11x2 + -11x2
19x + -1x2 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
19x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(19 + -1x) = 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 '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {0, 19}

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