x(2x-3)=5x

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


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

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

Solving
-3x + 2x2 = 5x

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-4 + x) = 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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4
Solution
x = {0, 4}

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