128-x^2=3x-2

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Solution for 128-x^2=3x-2 equation: 


Simplifying
128 + -1x2 = 3x + -2

Reorder the terms:
128 + -1x2 = -2 + 3x

Solving
128 + -1x2 = -2 + 3x

Solving for variable 'x'.

Reorder the terms:
128 + 2 + -3x + -1x2 = -2 + 3x + 2 + -3x

Combine like terms: 128 + 2 = 130
130 + -3x + -1x2 = -2 + 3x + 2 + -3x

Reorder the terms:
130 + -3x + -1x2 = -2 + 2 + 3x + -3x

Combine like terms: -2 + 2 = 0
130 + -3x + -1x2 = 0 + 3x + -3x
130 + -3x + -1x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
130 + -3x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(13 + x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13
Solution
x = {10, -13}

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