x^2-5x+19=4x+5

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Solution for x^2-5x+19=4x+5 equation: 


Simplifying
x2 + -5x + 19 = 4x + 5

Reorder the terms:
19 + -5x + x2 = 4x + 5

Reorder the terms:
19 + -5x + x2 = 5 + 4x

Solving
19 + -5x + x2 = 5 + 4x

Solving for variable 'x'.

Reorder the terms:
19 + -5 + -5x + -4x + x2 = 5 + 4x + -5 + -4x

Combine like terms: 19 + -5 = 14
14 + -5x + -4x + x2 = 5 + 4x + -5 + -4x

Combine like terms: -5x + -4x = -9x
14 + -9x + x2 = 5 + 4x + -5 + -4x

Reorder the terms:
14 + -9x + x2 = 5 + -5 + 4x + -4x

Combine like terms: 5 + -5 = 0
14 + -9x + x2 = 0 + 4x + -4x
14 + -9x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
14 + -9x + x2 = 0

Factor a trinomial.
(2 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2, 7}

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