4x^2-31x-11=-3

Solution for 4x^2-31x-11=-3 equation:

Simplifying
4x2 + -31x + -11 = -3

Reorder the terms:
-11 + -31x + 4x2 = -3

Solving
-11 + -31x + 4x2 = -3

Solving for variable 'x'.

Reorder the terms:
-11 + 3 + -31x + 4x2 = -3 + 3

Combine like terms: -11 + 3 = -8
-8 + -31x + 4x2 = -3 + 3

Combine like terms: -3 + 3 = 0
-8 + -31x + 4x2 = 0

Factor a trinomial.
(-1 + -4x)(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-0.25, 8}