2x^2-42x=-40

Solution for 2x^2-42x=-40 equation:

Simplifying
2x2 + -42x = -40

Reorder the terms:
-42x + 2x2 = -40

Solving
-42x + 2x2 = -40

Solving for variable 'x'.

Reorder the terms:
40 + -42x + 2x2 = -40 + 40

Combine like terms: -40 + 40 = 0
40 + -42x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -21x + x2) = 0

Factor a trinomial.
2((1 + -1x)(20 + -1x)) = 0

Ignore the factor 2.
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 '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {1, 20}