(23+x)*x=(12x+7)*2x

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Solution for (23+x)*x=(12x+7)*2x equation: 


Simplifying
(23 + x) * x = (12x + 7) * 2x

Reorder the terms for easier multiplication:
x(23 + x) = (12x + 7) * 2x
(23 * x + x * x) = (12x + 7) * 2x
(23x + x2) = (12x + 7) * 2x

Reorder the terms:
23x + x2 = (7 + 12x) * 2x

Reorder the terms for easier multiplication:
23x + x2 = 2x(7 + 12x)
23x + x2 = (7 * 2x + 12x * 2x)
23x + x2 = (14x + 24x2)

Solving
23x + x2 = 14x + 24x2

Solving for variable 'x'.

Reorder the terms:
23x + -14x + x2 + -24x2 = 14x + 24x2 + -14x + -24x2

Combine like terms: 23x + -14x = 9x
9x + x2 + -24x2 = 14x + 24x2 + -14x + -24x2

Combine like terms: x2 + -24x2 = -23x2
9x + -23x2 = 14x + 24x2 + -14x + -24x2

Reorder the terms:
9x + -23x2 = 14x + -14x + 24x2 + -24x2

Combine like terms: 14x + -14x = 0
9x + -23x2 = 0 + 24x2 + -24x2
9x + -23x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
9x + -23x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + -23x) = 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 '(9 + -23x)' equal to zero and attempt to solve:

Simplifying
9 + -23x = 0

Solving
9 + -23x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -23x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -23x = 0 + -9
-23x = 0 + -9

Combine like terms: 0 + -9 = -9
-23x = -9

Divide each side by '-23'.
x = 0.3913043478

Simplifying
x = 0.3913043478
Solution
x = {0, 0.3913043478}

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