8x^2+13x+17=7x^2-25

Solution for 8x^2+13x+17=7x^2-25 equation:

Simplifying
8x2 + 13x + 17 = 7x2 + -25

Reorder the terms:
17 + 13x + 8x2 = 7x2 + -25

Reorder the terms:
17 + 13x + 8x2 = -25 + 7x2

Solving
17 + 13x + 8x2 = -25 + 7x2

Solving for variable 'x'.

Reorder the terms:
17 + 25 + 13x + 8x2 + -7x2 = -25 + 7x2 + 25 + -7x2

Combine like terms: 17 + 25 = 42
42 + 13x + 8x2 + -7x2 = -25 + 7x2 + 25 + -7x2

Combine like terms: 8x2 + -7x2 = 1x2
42 + 13x + 1x2 = -25 + 7x2 + 25 + -7x2

Reorder the terms:
42 + 13x + 1x2 = -25 + 25 + 7x2 + -7x2

Combine like terms: -25 + 25 = 0
42 + 13x + 1x2 = 0 + 7x2 + -7x2
42 + 13x + 1x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
42 + 13x + 1x2 = 0

Factor a trinomial.
(7 + x)(6 + x) = 0

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-7, -6}