(x+5)(5x-1)=22x+2x^2

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Solution for (x+5)(5x-1)=22x+2x^2 equation: 


Simplifying
(x + 5)(5x + -1) = 22x + 2x2

Reorder the terms:
(5 + x)(5x + -1) = 22x + 2x2

Reorder the terms:
(5 + x)(-1 + 5x) = 22x + 2x2

Multiply (5 + x) * (-1 + 5x)
(5(-1 + 5x) + x(-1 + 5x)) = 22x + 2x2
((-1 * 5 + 5x * 5) + x(-1 + 5x)) = 22x + 2x2
((-5 + 25x) + x(-1 + 5x)) = 22x + 2x2
(-5 + 25x + (-1 * x + 5x * x)) = 22x + 2x2
(-5 + 25x + (-1x + 5x2)) = 22x + 2x2

Combine like terms: 25x + -1x = 24x
(-5 + 24x + 5x2) = 22x + 2x2

Solving
-5 + 24x + 5x2 = 22x + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 24x + -22x + 5x2 + -2x2 = 22x + 2x2 + -22x + -2x2

Combine like terms: 24x + -22x = 2x
-5 + 2x + 5x2 + -2x2 = 22x + 2x2 + -22x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-5 + 2x + 3x2 = 22x + 2x2 + -22x + -2x2

Reorder the terms:
-5 + 2x + 3x2 = 22x + -22x + 2x2 + -2x2

Combine like terms: 22x + -22x = 0
-5 + 2x + 3x2 = 0 + 2x2 + -2x2
-5 + 2x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 2x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(1 + -1x) = 0


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

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

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

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

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
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
Solution
x = {-1.666666667, 1}

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