x^2+11x-65=8x+5

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Solution for x^2+11x-65=8x+5 equation: 


Simplifying
x2 + 11x + -65 = 8x + 5

Reorder the terms:
-65 + 11x + x2 = 8x + 5

Reorder the terms:
-65 + 11x + x2 = 5 + 8x

Solving
-65 + 11x + x2 = 5 + 8x

Solving for variable 'x'.

Reorder the terms:
-65 + -5 + 11x + -8x + x2 = 5 + 8x + -5 + -8x

Combine like terms: -65 + -5 = -70
-70 + 11x + -8x + x2 = 5 + 8x + -5 + -8x

Combine like terms: 11x + -8x = 3x
-70 + 3x + x2 = 5 + 8x + -5 + -8x

Reorder the terms:
-70 + 3x + x2 = 5 + -5 + 8x + -8x

Combine like terms: 5 + -5 = 0
-70 + 3x + x2 = 0 + 8x + -8x
-70 + 3x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-70 + 3x + x2 = 0

Factor a trinomial.
(-10 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

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 = {-10, 7}

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