2x^2-(4x+5)=43

Solution for 2x^2-(4x+5)=43 equation:

Simplifying
2x2 + -1(4x + 5) = 43

Reorder the terms:
2x2 + -1(5 + 4x) = 43
2x2 + (5 * -1 + 4x * -1) = 43
2x2 + (-5 + -4x) = 43

Reorder the terms:
-5 + -4x + 2x2 = 43

Solving
-5 + -4x + 2x2 = 43

Solving for variable 'x'.

Reorder the terms:
-5 + -43 + -4x + 2x2 = 43 + -43

Combine like terms: -5 + -43 = -48
-48 + -4x + 2x2 = 43 + -43

Combine like terms: 43 + -43 = 0
-48 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -2x + x2) = 0

Factor a trinomial.
2((-4 + -1x)(6 + -1x)) = 0

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4, 6}