7x^2+5+12x=0

Solution for 7x^2+5+12x=0 equation:

Simplifying
7x2 + 5 + 12x = 0

Reorder the terms:
5 + 12x + 7x2 = 0

Solving
5 + 12x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + x)(5 + 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 '(5 + 7x)' equal to zero and attempt to solve:

Simplifying
5 + 7x = 0

Solving
5 + 7x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 7x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7x = 0 + -5
7x = 0 + -5

Combine like terms: 0 + -5 = -5
7x = -5

Divide each side by '7'.
x = -0.7142857143

Simplifying
x = -0.7142857143
Solution
x = {-1, -0.7142857143}