x^2-3x-19=7x+5

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Solution for x^2-3x-19=7x+5 equation: 


Simplifying
x2 + -3x + -19 = 7x + 5

Reorder the terms:
-19 + -3x + x2 = 7x + 5

Reorder the terms:
-19 + -3x + x2 = 5 + 7x

Solving
-19 + -3x + x2 = 5 + 7x

Solving for variable 'x'.

Reorder the terms:
-19 + -5 + -3x + -7x + x2 = 5 + 7x + -5 + -7x

Combine like terms: -19 + -5 = -24
-24 + -3x + -7x + x2 = 5 + 7x + -5 + -7x

Combine like terms: -3x + -7x = -10x
-24 + -10x + x2 = 5 + 7x + -5 + -7x

Reorder the terms:
-24 + -10x + x2 = 5 + -5 + 7x + -7x

Combine like terms: 5 + -5 = 0
-24 + -10x + x2 = 0 + 7x + -7x
-24 + -10x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-24 + -10x + x2 = 0

Factor a trinomial.
(-2 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-2, 12}

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