7x^2+17x-7=5-8x

Solution for 7x^2+17x-7=5-8x equation:

Simplifying
7x2 + 17x + -7 = 5 + -8x

Reorder the terms:
-7 + 17x + 7x2 = 5 + -8x

Solving
-7 + 17x + 7x2 = 5 + -8x

Solving for variable 'x'.

Reorder the terms:
-7 + -5 + 17x + 8x + 7x2 = 5 + -8x + -5 + 8x

Combine like terms: -7 + -5 = -12
-12 + 17x + 8x + 7x2 = 5 + -8x + -5 + 8x

Combine like terms: 17x + 8x = 25x
-12 + 25x + 7x2 = 5 + -8x + -5 + 8x

Reorder the terms:
-12 + 25x + 7x2 = 5 + -5 + -8x + 8x

Combine like terms: 5 + -5 = 0
-12 + 25x + 7x2 = 0 + -8x + 8x
-12 + 25x + 7x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-12 + 25x + 7x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -7x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-4, 0.4285714286}