(3x-2)(x-9)=(x+7)(1-2x)

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Solution for (3x-2)(x-9)=(x+7)(1-2x) equation: 


Simplifying
(3x + -2)(x + -9) = (x + 7)(1 + -2x)

Reorder the terms:
(-2 + 3x)(x + -9) = (x + 7)(1 + -2x)

Reorder the terms:
(-2 + 3x)(-9 + x) = (x + 7)(1 + -2x)

Multiply (-2 + 3x) * (-9 + x)
(-2(-9 + x) + 3x * (-9 + x)) = (x + 7)(1 + -2x)
((-9 * -2 + x * -2) + 3x * (-9 + x)) = (x + 7)(1 + -2x)
((18 + -2x) + 3x * (-9 + x)) = (x + 7)(1 + -2x)
(18 + -2x + (-9 * 3x + x * 3x)) = (x + 7)(1 + -2x)
(18 + -2x + (-27x + 3x2)) = (x + 7)(1 + -2x)

Combine like terms: -2x + -27x = -29x
(18 + -29x + 3x2) = (x + 7)(1 + -2x)

Reorder the terms:
18 + -29x + 3x2 = (7 + x)(1 + -2x)

Multiply (7 + x) * (1 + -2x)
18 + -29x + 3x2 = (7(1 + -2x) + x(1 + -2x))
18 + -29x + 3x2 = ((1 * 7 + -2x * 7) + x(1 + -2x))
18 + -29x + 3x2 = ((7 + -14x) + x(1 + -2x))
18 + -29x + 3x2 = (7 + -14x + (1 * x + -2x * x))
18 + -29x + 3x2 = (7 + -14x + (1x + -2x2))

Combine like terms: -14x + 1x = -13x
18 + -29x + 3x2 = (7 + -13x + -2x2)

Solving
18 + -29x + 3x2 = 7 + -13x + -2x2

Solving for variable 'x'.

Reorder the terms:
18 + -7 + -29x + 13x + 3x2 + 2x2 = 7 + -13x + -2x2 + -7 + 13x + 2x2

Combine like terms: 18 + -7 = 11
11 + -29x + 13x + 3x2 + 2x2 = 7 + -13x + -2x2 + -7 + 13x + 2x2

Combine like terms: -29x + 13x = -16x
11 + -16x + 3x2 + 2x2 = 7 + -13x + -2x2 + -7 + 13x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
11 + -16x + 5x2 = 7 + -13x + -2x2 + -7 + 13x + 2x2

Reorder the terms:
11 + -16x + 5x2 = 7 + -7 + -13x + 13x + -2x2 + 2x2

Combine like terms: 7 + -7 = 0
11 + -16x + 5x2 = 0 + -13x + 13x + -2x2 + 2x2
11 + -16x + 5x2 = -13x + 13x + -2x2 + 2x2

Combine like terms: -13x + 13x = 0
11 + -16x + 5x2 = 0 + -2x2 + 2x2
11 + -16x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
11 + -16x + 5x2 = 0

Factor a trinomial.
(1 + -1x)(11 + -5x) = 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 '(11 + -5x)' equal to zero and attempt to solve:

Simplifying
11 + -5x = 0

Solving
11 + -5x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -5x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5x = 0 + -11
-5x = 0 + -11

Combine like terms: 0 + -11 = -11
-5x = -11

Divide each side by '-5'.
x = 2.2

Simplifying
x = 2.2
Solution
x = {1, 2.2}

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