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

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


Simplifying
7(3x + 2) * 2(2 + -1x) * 2 + (3x + 2)(1 + -1x) = 0

Reorder the terms:
7(2 + 3x) * 2(2 + -1x) * 2 + (3x + 2)(1 + -1x) = 0

Reorder the terms for easier multiplication:
7 * 2 * 2(2 + 3x)(2 + -1x) + (3x + 2)(1 + -1x) = 0

Multiply 7 * 2
14 * 2(2 + 3x)(2 + -1x) + (3x + 2)(1 + -1x) = 0

Multiply 14 * 2
28(2 + 3x)(2 + -1x) + (3x + 2)(1 + -1x) = 0

Multiply (2 + 3x) * (2 + -1x)
28(2(2 + -1x) + 3x * (2 + -1x)) + (3x + 2)(1 + -1x) = 0
28((2 * 2 + -1x * 2) + 3x * (2 + -1x)) + (3x + 2)(1 + -1x) = 0
28((4 + -2x) + 3x * (2 + -1x)) + (3x + 2)(1 + -1x) = 0
28(4 + -2x + (2 * 3x + -1x * 3x)) + (3x + 2)(1 + -1x) = 0
28(4 + -2x + (6x + -3x2)) + (3x + 2)(1 + -1x) = 0

Combine like terms: -2x + 6x = 4x
28(4 + 4x + -3x2) + (3x + 2)(1 + -1x) = 0
(4 * 28 + 4x * 28 + -3x2 * 28) + (3x + 2)(1 + -1x) = 0
(112 + 112x + -84x2) + (3x + 2)(1 + -1x) = 0

Reorder the terms:
112 + 112x + -84x2 + (2 + 3x)(1 + -1x) = 0

Multiply (2 + 3x) * (1 + -1x)
112 + 112x + -84x2 + (2(1 + -1x) + 3x * (1 + -1x)) = 0
112 + 112x + -84x2 + ((1 * 2 + -1x * 2) + 3x * (1 + -1x)) = 0
112 + 112x + -84x2 + ((2 + -2x) + 3x * (1 + -1x)) = 0
112 + 112x + -84x2 + (2 + -2x + (1 * 3x + -1x * 3x)) = 0
112 + 112x + -84x2 + (2 + -2x + (3x + -3x2)) = 0

Combine like terms: -2x + 3x = 1x
112 + 112x + -84x2 + (2 + 1x + -3x2) = 0

Reorder the terms:
112 + 2 + 112x + 1x + -84x2 + -3x2 = 0

Combine like terms: 112 + 2 = 114
114 + 112x + 1x + -84x2 + -3x2 = 0

Combine like terms: 112x + 1x = 113x
114 + 113x + -84x2 + -3x2 = 0

Combine like terms: -84x2 + -3x2 = -87x2
114 + 113x + -87x2 = 0

Solving
114 + 113x + -87x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(57 + -29x)(2 + 3x) = 0


Subproblem 1
Set the factor '(57 + -29x)' equal to zero and attempt to solve:

Simplifying
57 + -29x = 0

Solving
57 + -29x = 0

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

Add '-57' to each side of the equation.
57 + -57 + -29x = 0 + -57

Combine like terms: 57 + -57 = 0
0 + -29x = 0 + -57
-29x = 0 + -57

Combine like terms: 0 + -57 = -57
-29x = -57

Divide each side by '-29'.
x = 1.965517241

Simplifying
x = 1.965517241

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 = {1.965517241, -0.6666666667}

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