x^2-15x-6=-7x+3

Solution for x^2-15x-6=-7x+3 equation:

Simplifying
x2 + -15x + -6 = -7x + 3

Reorder the terms:
-6 + -15x + x2 = -7x + 3

Reorder the terms:
-6 + -15x + x2 = 3 + -7x

Solving
-6 + -15x + x2 = 3 + -7x

Solving for variable 'x'.

Reorder the terms:
-6 + -3 + -15x + 7x + x2 = 3 + -7x + -3 + 7x

Combine like terms: -6 + -3 = -9
-9 + -15x + 7x + x2 = 3 + -7x + -3 + 7x

Combine like terms: -15x + 7x = -8x
-9 + -8x + x2 = 3 + -7x + -3 + 7x

Reorder the terms:
-9 + -8x + x2 = 3 + -3 + -7x + 7x

Combine like terms: 3 + -3 = 0
-9 + -8x + x2 = 0 + -7x + 7x
-9 + -8x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-9 + -8x + x2 = 0

Factor a trinomial.
(-1 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1, 9}