0=4x^2+11x+6

Solution for 0=4x^2+11x+6 equation:

Simplifying
0 = 4x2 + 11x + 6

Reorder the terms:
0 = 6 + 11x + 4x2

Solving
0 = 6 + 11x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -11x + -4x2 = 6 + 11x + 4x2 + -6 + -11x + -4x2

Reorder the terms:
-6 + -11x + -4x2 = 6 + -6 + 11x + -11x + 4x2 + -4x2

Combine like terms: 6 + -6 = 0
-6 + -11x + -4x2 = 0 + 11x + -11x + 4x2 + -4x2
-6 + -11x + -4x2 = 11x + -11x + 4x2 + -4x2

Combine like terms: 11x + -11x = 0
-6 + -11x + -4x2 = 0 + 4x2 + -4x2
-6 + -11x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + -11x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 11x + 4x2) = 0

Factor a trinomial.
-1((2 + x)(3 + 4x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {-2, -0.75}