5x(4x+1)=4x+1

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Solution for 5x(4x+1)=4x+1 equation: 


Simplifying
5x(4x + 1) = 4x + 1

Reorder the terms:
5x(1 + 4x) = 4x + 1
(1 * 5x + 4x * 5x) = 4x + 1
(5x + 20x2) = 4x + 1

Reorder the terms:
5x + 20x2 = 1 + 4x

Solving
5x + 20x2 = 1 + 4x

Solving for variable 'x'.

Reorder the terms:
-1 + 5x + -4x + 20x2 = 1 + 4x + -1 + -4x

Combine like terms: 5x + -4x = 1x
-1 + 1x + 20x2 = 1 + 4x + -1 + -4x

Reorder the terms:
-1 + 1x + 20x2 = 1 + -1 + 4x + -4x

Combine like terms: 1 + -1 = 0
-1 + 1x + 20x2 = 0 + 4x + -4x
-1 + 1x + 20x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-1 + 1x + 20x2 = 0

Factor a trinomial.
(-1 + -4x)(1 + -5x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-0.25, 0.2}

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