112=2x^2+4x*5

Solution for 112=2x^2+4x*5 equation:

Simplifying
112 = 2x2 + 4x * 5

Reorder the terms for easier multiplication:
112 = 2x2 + 4 * 5x

Multiply 4 * 5
112 = 2x2 + 20x

Reorder the terms:
112 = 20x + 2x2

Solving
112 = 20x + 2x2

Solving for variable 'x'.

Reorder the terms:
112 + -20x + -2x2 = 20x + -20x + 2x2 + -2x2

Combine like terms: 20x + -20x = 0
112 + -20x + -2x2 = 0 + 2x2 + -2x2
112 + -20x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
112 + -20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(56 + -10x + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(14 + x)) = 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 '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Solution
x = {4, -14}