5x(x-4)-17=4x(x-1)

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Solution for 5x(x-4)-17=4x(x-1) equation: 


Simplifying
5x(x + -4) + -17 = 4x(x + -1)

Reorder the terms:
5x(-4 + x) + -17 = 4x(x + -1)
(-4 * 5x + x * 5x) + -17 = 4x(x + -1)
(-20x + 5x2) + -17 = 4x(x + -1)

Reorder the terms:
-17 + -20x + 5x2 = 4x(x + -1)

Reorder the terms:
-17 + -20x + 5x2 = 4x(-1 + x)
-17 + -20x + 5x2 = (-1 * 4x + x * 4x)
-17 + -20x + 5x2 = (-4x + 4x2)

Solving
-17 + -20x + 5x2 = -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
-17 + -20x + 4x + 5x2 + -4x2 = -4x + 4x2 + 4x + -4x2

Combine like terms: -20x + 4x = -16x
-17 + -16x + 5x2 + -4x2 = -4x + 4x2 + 4x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-17 + -16x + 1x2 = -4x + 4x2 + 4x + -4x2

Reorder the terms:
-17 + -16x + 1x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
-17 + -16x + 1x2 = 0 + 4x2 + -4x2
-17 + -16x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-17 + -16x + 1x2 = 0

Factor a trinomial.
(-1 + -1x)(17 + -1x) = 0


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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-1, 17}

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