0=7x^2+8x+1

Solution for 0=7x^2+8x+1 equation:

Simplifying
0 = 7x2 + 8x + 1

Reorder the terms:
0 = 1 + 8x + 7x2

Solving
0 = 1 + 8x + 7x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 8x + 7x2) = 0

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

Ignore the factor -1.
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}