4-3x(x-9)=22-2x

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Solution for 4-3x(x-9)=22-2x equation: 


Simplifying
4 + -3x(x + -9) = 22 + -2x

Reorder the terms:
4 + -3x(-9 + x) = 22 + -2x
4 + (-9 * -3x + x * -3x) = 22 + -2x
4 + (27x + -3x2) = 22 + -2x

Solving
4 + 27x + -3x2 = 22 + -2x

Solving for variable 'x'.

Reorder the terms:
4 + -22 + 27x + 2x + -3x2 = 22 + -2x + -22 + 2x

Combine like terms: 4 + -22 = -18
-18 + 27x + 2x + -3x2 = 22 + -2x + -22 + 2x

Combine like terms: 27x + 2x = 29x
-18 + 29x + -3x2 = 22 + -2x + -22 + 2x

Reorder the terms:
-18 + 29x + -3x2 = 22 + -22 + -2x + 2x

Combine like terms: 22 + -22 = 0
-18 + 29x + -3x2 = 0 + -2x + 2x
-18 + 29x + -3x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-18 + 29x + -3x2 = 0

Factor a trinomial.
(-9 + x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {9, 0.6666666667}

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