(14x^2-9)+(11x+6)=0

Solution for (14x^2-9)+(11x+6)=0 equation:

Simplifying
(14x2 + -9) + (11x + 6) = 0

Reorder the terms:
(-9 + 14x2) + (11x + 6) = 0

Remove parenthesis around (-9 + 14x2)
-9 + 14x2 + (11x + 6) = 0

Reorder the terms:
-9 + 14x2 + (6 + 11x) = 0

Remove parenthesis around (6 + 11x)
-9 + 14x2 + 6 + 11x = 0

Reorder the terms:
-9 + 6 + 11x + 14x2 = 0

Combine like terms: -9 + 6 = -3
-3 + 11x + 14x2 = 0

Solving
-3 + 11x + 14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(3 + -14x) = 0

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(3 + -14x)' equal to zero and attempt to solve:

Simplifying
3 + -14x = 0

Solving
3 + -14x = 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 + -14x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -14x = 0 + -3
-14x = 0 + -3

Combine like terms: 0 + -3 = -3
-14x = -3

Divide each side by '-14'.
x = 0.2142857143

Simplifying
x = 0.2142857143
Solution
x = {-1, 0.2142857143}