x^2-2x-15=7x-5

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Solution for x^2-2x-15=7x-5 equation: 


Simplifying
x2 + -2x + -15 = 7x + -5

Reorder the terms:
-15 + -2x + x2 = 7x + -5

Reorder the terms:
-15 + -2x + x2 = -5 + 7x

Solving
-15 + -2x + x2 = -5 + 7x

Solving for variable 'x'.

Reorder the terms:
-15 + 5 + -2x + -7x + x2 = -5 + 7x + 5 + -7x

Combine like terms: -15 + 5 = -10
-10 + -2x + -7x + x2 = -5 + 7x + 5 + -7x

Combine like terms: -2x + -7x = -9x
-10 + -9x + x2 = -5 + 7x + 5 + -7x

Reorder the terms:
-10 + -9x + x2 = -5 + 5 + 7x + -7x

Combine like terms: -5 + 5 = 0
-10 + -9x + x2 = 0 + 7x + -7x
-10 + -9x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-10 + -9x + x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1, 10}

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