(5x-2)(5x-2)=(6x-1)(x-4)

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Solution for (5x-2)(5x-2)=(6x-1)(x-4) equation: 


Simplifying
(5x + -2)(5x + -2) = (6x + -1)(x + -4)

Reorder the terms:
(-2 + 5x)(5x + -2) = (6x + -1)(x + -4)

Reorder the terms:
(-2 + 5x)(-2 + 5x) = (6x + -1)(x + -4)

Multiply (-2 + 5x) * (-2 + 5x)
(-2(-2 + 5x) + 5x * (-2 + 5x)) = (6x + -1)(x + -4)
((-2 * -2 + 5x * -2) + 5x * (-2 + 5x)) = (6x + -1)(x + -4)
((4 + -10x) + 5x * (-2 + 5x)) = (6x + -1)(x + -4)
(4 + -10x + (-2 * 5x + 5x * 5x)) = (6x + -1)(x + -4)
(4 + -10x + (-10x + 25x2)) = (6x + -1)(x + -4)

Combine like terms: -10x + -10x = -20x
(4 + -20x + 25x2) = (6x + -1)(x + -4)

Reorder the terms:
4 + -20x + 25x2 = (-1 + 6x)(x + -4)

Reorder the terms:
4 + -20x + 25x2 = (-1 + 6x)(-4 + x)

Multiply (-1 + 6x) * (-4 + x)
4 + -20x + 25x2 = (-1(-4 + x) + 6x * (-4 + x))
4 + -20x + 25x2 = ((-4 * -1 + x * -1) + 6x * (-4 + x))
4 + -20x + 25x2 = ((4 + -1x) + 6x * (-4 + x))
4 + -20x + 25x2 = (4 + -1x + (-4 * 6x + x * 6x))
4 + -20x + 25x2 = (4 + -1x + (-24x + 6x2))

Combine like terms: -1x + -24x = -25x
4 + -20x + 25x2 = (4 + -25x + 6x2)

Add '-4' to each side of the equation.
4 + -20x + -4 + 25x2 = 4 + -25x + -4 + 6x2

Reorder the terms:
4 + -4 + -20x + 25x2 = 4 + -25x + -4 + 6x2

Combine like terms: 4 + -4 = 0
0 + -20x + 25x2 = 4 + -25x + -4 + 6x2
-20x + 25x2 = 4 + -25x + -4 + 6x2

Reorder the terms:
-20x + 25x2 = 4 + -4 + -25x + 6x2

Combine like terms: 4 + -4 = 0
-20x + 25x2 = 0 + -25x + 6x2
-20x + 25x2 = -25x + 6x2

Solving
-20x + 25x2 = -25x + 6x2

Solving for variable 'x'.

Reorder the terms:
-20x + 25x + 25x2 + -6x2 = -25x + 6x2 + 25x + -6x2

Combine like terms: -20x + 25x = 5x
5x + 25x2 + -6x2 = -25x + 6x2 + 25x + -6x2

Combine like terms: 25x2 + -6x2 = 19x2
5x + 19x2 = -25x + 6x2 + 25x + -6x2

Reorder the terms:
5x + 19x2 = -25x + 25x + 6x2 + -6x2

Combine like terms: -25x + 25x = 0
5x + 19x2 = 0 + 6x2 + -6x2
5x + 19x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5x + 19x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + 19x) = 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 '(5 + 19x)' equal to zero and attempt to solve:

Simplifying
5 + 19x = 0

Solving
5 + 19x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 19x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 19x = 0 + -5
19x = 0 + -5

Combine like terms: 0 + -5 = -5
19x = -5

Divide each side by '19'.
x = -0.2631578947

Simplifying
x = -0.2631578947
Solution
x = {0, -0.2631578947}

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