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

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


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

Remove parenthesis around (4x)
5x + 4 * 4x = 2((5x + 4)(2x))

Multiply 4 * 4
5x + 16x = 2((5x + 4)(2x))

Combine like terms: 5x + 16x = 21x
21x = 2((5x + 4)(2x))

Reorder the terms:
21x = 2((4 + 5x)(2x))

Remove parenthesis around (2x)
21x = 2((4 + 5x) * 2x)

Reorder the terms for easier multiplication:
21x = 2(2x(4 + 5x))
21x = 2((4 * 2x + 5x * 2x))
21x = 2((8x + 10x2))
21x = (8x * 2 + 10x2 * 2)
21x = (16x + 20x2)

Solving
21x = 16x + 20x2

Solving for variable 'x'.

Combine like terms: 21x + -16x = 5x
5x + -20x2 = 16x + 20x2 + -16x + -20x2

Reorder the terms:
5x + -20x2 = 16x + -16x + 20x2 + -20x2

Combine like terms: 16x + -16x = 0
5x + -20x2 = 0 + 20x2 + -20x2
5x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
5x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(1 + -4x) = 0

Ignore the factor 5.

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 '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, 0.25}

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