4x^2-4x-3=5

Solution for 4x^2-4x-3=5 equation:

Simplifying
4x2 + -4x + -3 = 5

Reorder the terms:
-3 + -4x + 4x2 = 5

Solving
-3 + -4x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
-3 + -5 + -4x + 4x2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + -4x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -1x + x2) = 0

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

Ignore the factor 4.
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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}