-0.5x^2-4x+300=0.5x^2-2x+76

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Solution for -0.5x^2-4x+300=0.5x^2-2x+76 equation: 


Simplifying
-0.5x2 + -4x + 300 = 0.5x2 + -2x + 76

Reorder the terms:
300 + -4x + -0.5x2 = 0.5x2 + -2x + 76

Reorder the terms:
300 + -4x + -0.5x2 = 76 + -2x + 0.5x2

Solving
300 + -4x + -0.5x2 = 76 + -2x + 0.5x2

Solving for variable 'x'.

Reorder the terms:
300 + -76 + -4x + 2x + -0.5x2 + -0.5x2 = 76 + -2x + 0.5x2 + -76 + 2x + -0.5x2

Combine like terms: 300 + -76 = 224
224 + -4x + 2x + -0.5x2 + -0.5x2 = 76 + -2x + 0.5x2 + -76 + 2x + -0.5x2

Combine like terms: -4x + 2x = -2x
224 + -2x + -0.5x2 + -0.5x2 = 76 + -2x + 0.5x2 + -76 + 2x + -0.5x2

Combine like terms: -0.5x2 + -0.5x2 = -1x2
224 + -2x + -1x2 = 76 + -2x + 0.5x2 + -76 + 2x + -0.5x2

Reorder the terms:
224 + -2x + -1x2 = 76 + -76 + -2x + 2x + 0.5x2 + -0.5x2

Combine like terms: 76 + -76 = 0
224 + -2x + -1x2 = 0 + -2x + 2x + 0.5x2 + -0.5x2
224 + -2x + -1x2 = -2x + 2x + 0.5x2 + -0.5x2

Combine like terms: -2x + 2x = 0
224 + -2x + -1x2 = 0 + 0.5x2 + -0.5x2
224 + -2x + -1x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
224 + -2x + -1x2 = 0.0

Factor a trinomial.
(14 + -1x)(16 + x) = 0.0


Subproblem 1
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 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 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14

Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {14, -16}

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