3=4x^2+11x

Solution for 3=4x^2+11x equation:

Simplifying
3 = 4x2 + 11x

Reorder the terms:
3 = 11x + 4x2

Solving
3 = 11x + 4x2

Solving for variable 'x'.

Reorder the terms:
3 + -11x + -4x2 = 11x + -11x + 4x2 + -4x2

Combine like terms: 11x + -11x = 0
3 + -11x + -4x2 = 0 + 4x2 + -4x2
3 + -11x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3 + -11x + -4x2 = 0

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

Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {0.25, -3}