23-(8x^2+12x)=3x^2-3x+3

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Solution for 23-(8x^2+12x)=3x^2-3x+3 equation: 


Simplifying
23 + -1(8x2 + 12x) = 3x2 + -3x + 3

Reorder the terms:
23 + -1(12x + 8x2) = 3x2 + -3x + 3
23 + (12x * -1 + 8x2 * -1) = 3x2 + -3x + 3
23 + (-12x + -8x2) = 3x2 + -3x + 3

Reorder the terms:
23 + -12x + -8x2 = 3 + -3x + 3x2

Solving
23 + -12x + -8x2 = 3 + -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
23 + -3 + -12x + 3x + -8x2 + -3x2 = 3 + -3x + 3x2 + -3 + 3x + -3x2

Combine like terms: 23 + -3 = 20
20 + -12x + 3x + -8x2 + -3x2 = 3 + -3x + 3x2 + -3 + 3x + -3x2

Combine like terms: -12x + 3x = -9x
20 + -9x + -8x2 + -3x2 = 3 + -3x + 3x2 + -3 + 3x + -3x2

Combine like terms: -8x2 + -3x2 = -11x2
20 + -9x + -11x2 = 3 + -3x + 3x2 + -3 + 3x + -3x2

Reorder the terms:
20 + -9x + -11x2 = 3 + -3 + -3x + 3x + 3x2 + -3x2

Combine like terms: 3 + -3 = 0
20 + -9x + -11x2 = 0 + -3x + 3x + 3x2 + -3x2
20 + -9x + -11x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
20 + -9x + -11x2 = 0 + 3x2 + -3x2
20 + -9x + -11x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
20 + -9x + -11x2 = 0

Factor a trinomial.
(1 + -1x)(20 + 11x) = 0


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 + 11x)' equal to zero and attempt to solve:

Simplifying
20 + 11x = 0

Solving
20 + 11x = 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 + 11x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 11x = 0 + -20
11x = 0 + -20

Combine like terms: 0 + -20 = -20
11x = -20

Divide each side by '11'.
x = -1.818181818

Simplifying
x = -1.818181818
Solution
x = {1, -1.818181818}

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