2*(x^2)+20*x+52=100

Solution for 2*(x^2)+20*x+52=100 equation:

Simplifying
2(x2) + 20x + 52 = 100

Reorder the terms:
52 + 20x + 2x2 = 100

Solving
52 + 20x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
52 + -100 + 20x + 2x2 = 100 + -100

Combine like terms: 52 + -100 = -48
-48 + 20x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-48 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 10x + x2) = 0

Factor a trinomial.
2((-12 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
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 = {-12, 2}