(5x-4)*(5x-4)+(5x-4)=0

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Solution for (5x-4)*(5x-4)+(5x-4)=0 equation: 


Simplifying
(5x + -4)(5x + -4) + (5x + -4) = 0

Reorder the terms:
(-4 + 5x)(5x + -4) + (5x + -4) = 0

Reorder the terms:
(-4 + 5x)(-4 + 5x) + (5x + -4) = 0

Multiply (-4 + 5x) * (-4 + 5x)
(-4(-4 + 5x) + 5x * (-4 + 5x)) + (5x + -4) = 0
((-4 * -4 + 5x * -4) + 5x * (-4 + 5x)) + (5x + -4) = 0
((16 + -20x) + 5x * (-4 + 5x)) + (5x + -4) = 0
(16 + -20x + (-4 * 5x + 5x * 5x)) + (5x + -4) = 0
(16 + -20x + (-20x + 25x2)) + (5x + -4) = 0

Combine like terms: -20x + -20x = -40x
(16 + -40x + 25x2) + (5x + -4) = 0

Reorder the terms:
16 + -40x + 25x2 + (-4 + 5x) = 0

Remove parenthesis around (-4 + 5x)
16 + -40x + 25x2 + -4 + 5x = 0

Reorder the terms:
16 + -4 + -40x + 5x + 25x2 = 0

Combine like terms: 16 + -4 = 12
12 + -40x + 5x + 25x2 = 0

Combine like terms: -40x + 5x = -35x
12 + -35x + 25x2 = 0

Solving
12 + -35x + 25x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -5x)(4 + -5x) = 0


Subproblem 1
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6

Subproblem 2
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {0.6, 0.8}

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