5x(x-5)-22=4x(x-4)

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Solution for 5x(x-5)-22=4x(x-4) equation: 


Simplifying
5x(x + -5) + -22 = 4x(x + -4)

Reorder the terms:
5x(-5 + x) + -22 = 4x(x + -4)
(-5 * 5x + x * 5x) + -22 = 4x(x + -4)
(-25x + 5x2) + -22 = 4x(x + -4)

Reorder the terms:
-22 + -25x + 5x2 = 4x(x + -4)

Reorder the terms:
-22 + -25x + 5x2 = 4x(-4 + x)
-22 + -25x + 5x2 = (-4 * 4x + x * 4x)
-22 + -25x + 5x2 = (-16x + 4x2)

Solving
-22 + -25x + 5x2 = -16x + 4x2

Solving for variable 'x'.

Reorder the terms:
-22 + -25x + 16x + 5x2 + -4x2 = -16x + 4x2 + 16x + -4x2

Combine like terms: -25x + 16x = -9x
-22 + -9x + 5x2 + -4x2 = -16x + 4x2 + 16x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-22 + -9x + 1x2 = -16x + 4x2 + 16x + -4x2

Reorder the terms:
-22 + -9x + 1x2 = -16x + 16x + 4x2 + -4x2

Combine like terms: -16x + 16x = 0
-22 + -9x + 1x2 = 0 + 4x2 + -4x2
-22 + -9x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-22 + -9x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(11 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-2, 11}

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