x(9x+12)=4x^2-22x+48

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Solution for x(9x+12)=4x^2-22x+48 equation: 


Simplifying
x(9x + 12) = 4x2 + -22x + 48

Reorder the terms:
x(12 + 9x) = 4x2 + -22x + 48
(12 * x + 9x * x) = 4x2 + -22x + 48
(12x + 9x2) = 4x2 + -22x + 48

Reorder the terms:
12x + 9x2 = 48 + -22x + 4x2

Solving
12x + 9x2 = 48 + -22x + 4x2

Solving for variable 'x'.

Reorder the terms:
-48 + 12x + 22x + 9x2 + -4x2 = 48 + -22x + 4x2 + -48 + 22x + -4x2

Combine like terms: 12x + 22x = 34x
-48 + 34x + 9x2 + -4x2 = 48 + -22x + 4x2 + -48 + 22x + -4x2

Combine like terms: 9x2 + -4x2 = 5x2
-48 + 34x + 5x2 = 48 + -22x + 4x2 + -48 + 22x + -4x2

Reorder the terms:
-48 + 34x + 5x2 = 48 + -48 + -22x + 22x + 4x2 + -4x2

Combine like terms: 48 + -48 = 0
-48 + 34x + 5x2 = 0 + -22x + 22x + 4x2 + -4x2
-48 + 34x + 5x2 = -22x + 22x + 4x2 + -4x2

Combine like terms: -22x + 22x = 0
-48 + 34x + 5x2 = 0 + 4x2 + -4x2
-48 + 34x + 5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-48 + 34x + 5x2 = 0

Factor a trinomial.
(-8 + -1x)(6 + -5x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-8, 1.2}

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