5x=4x(2x-3)

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


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

Reorder the terms:
5x = 4x(-3 + 2x)
5x = (-3 * 4x + 2x * 4x)
5x = (-12x + 8x2)

Solving
5x = -12x + 8x2

Solving for variable 'x'.

Combine like terms: 5x + 12x = 17x
17x + -8x2 = -12x + 8x2 + 12x + -8x2

Reorder the terms:
17x + -8x2 = -12x + 12x + 8x2 + -8x2

Combine like terms: -12x + 12x = 0
17x + -8x2 = 0 + 8x2 + -8x2
17x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
17x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(17 + -8x) = 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 '(17 + -8x)' equal to zero and attempt to solve:

Simplifying
17 + -8x = 0

Solving
17 + -8x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -8x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -8x = 0 + -17
-8x = 0 + -17

Combine like terms: 0 + -17 = -17
-8x = -17

Divide each side by '-8'.
x = 2.125

Simplifying
x = 2.125
Solution
x = {0, 2.125}

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