x^2+15x-27=8x+3

Solution for x^2+15x-27=8x+3 equation:

Simplifying
x2 + 15x + -27 = 8x + 3

Reorder the terms:
-27 + 15x + x2 = 8x + 3

Reorder the terms:
-27 + 15x + x2 = 3 + 8x

Solving
-27 + 15x + x2 = 3 + 8x

Solving for variable 'x'.

Reorder the terms:
-27 + -3 + 15x + -8x + x2 = 3 + 8x + -3 + -8x

Combine like terms: -27 + -3 = -30
-30 + 15x + -8x + x2 = 3 + 8x + -3 + -8x

Combine like terms: 15x + -8x = 7x
-30 + 7x + x2 = 3 + 8x + -3 + -8x

Reorder the terms:
-30 + 7x + x2 = 3 + -3 + 8x + -8x

Combine like terms: 3 + -3 = 0
-30 + 7x + x2 = 0 + 8x + -8x
-30 + 7x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-30 + 7x + x2 = 0

Factor a trinomial.
(-10 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-10, 3}