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

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


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

Reorder the terms:
5x(4 + 2x) = 4x(3x + -5)
(4 * 5x + 2x * 5x) = 4x(3x + -5)
(20x + 10x2) = 4x(3x + -5)

Reorder the terms:
20x + 10x2 = 4x(-5 + 3x)
20x + 10x2 = (-5 * 4x + 3x * 4x)
20x + 10x2 = (-20x + 12x2)

Solving
20x + 10x2 = -20x + 12x2

Solving for variable 'x'.

Reorder the terms:
20x + 20x + 10x2 + -12x2 = -20x + 12x2 + 20x + -12x2

Combine like terms: 20x + 20x = 40x
40x + 10x2 + -12x2 = -20x + 12x2 + 20x + -12x2

Combine like terms: 10x2 + -12x2 = -2x2
40x + -2x2 = -20x + 12x2 + 20x + -12x2

Reorder the terms:
40x + -2x2 = -20x + 20x + 12x2 + -12x2

Combine like terms: -20x + 20x = 0
40x + -2x2 = 0 + 12x2 + -12x2
40x + -2x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
40x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(20 + -1x) = 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 '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {0, 20}

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