7x^2+1=-8x

Solution for 7x^2+1=-8x equation:

Simplifying
7x2 + 1 = -8x

Reorder the terms:
1 + 7x2 = -8x

Solving
1 + 7x2 = -8x

Solving for variable 'x'.

Reorder the terms:
1 + 8x + 7x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
1 + 8x + 7x2 = 0

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

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(1 + 7x)' equal to zero and attempt to solve:

Simplifying
1 + 7x = 0

Solving
1 + 7x = 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 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Divide each side by '7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Solution
x = {-1, -0.1428571429}