2x(3-x)-4(x+2)=3x(2-3)+5+7x-13

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Solution for 2x(3-x)-4(x+2)=3x(2-3)+5+7x-13 equation: 


Simplifying
2x(3 + -1x) + -4(x + 2) = 3x(2 + -3) + 5 + 7x + -13
(3 * 2x + -1x * 2x) + -4(x + 2) = 3x(2 + -3) + 5 + 7x + -13
(6x + -2x2) + -4(x + 2) = 3x(2 + -3) + 5 + 7x + -13

Reorder the terms:
6x + -2x2 + -4(2 + x) = 3x(2 + -3) + 5 + 7x + -13
6x + -2x2 + (2 * -4 + x * -4) = 3x(2 + -3) + 5 + 7x + -13
6x + -2x2 + (-8 + -4x) = 3x(2 + -3) + 5 + 7x + -13

Reorder the terms:
-8 + 6x + -4x + -2x2 = 3x(2 + -3) + 5 + 7x + -13

Combine like terms: 6x + -4x = 2x
-8 + 2x + -2x2 = 3x(2 + -3) + 5 + 7x + -13

Combine like terms: 2 + -3 = -1
-8 + 2x + -2x2 = 3x(-1) + 5 + 7x + -13

Reorder the terms for easier multiplication:
-8 + 2x + -2x2 = 3 * -1x + 5 + 7x + -13

Multiply 3 * -1
-8 + 2x + -2x2 = -3x + 5 + 7x + -13

Reorder the terms:
-8 + 2x + -2x2 = 5 + -13 + -3x + 7x

Combine like terms: 5 + -13 = -8
-8 + 2x + -2x2 = -8 + -3x + 7x

Combine like terms: -3x + 7x = 4x
-8 + 2x + -2x2 = -8 + 4x

Add '8' to each side of the equation.
-8 + 2x + 8 + -2x2 = -8 + 8 + 4x

Reorder the terms:
-8 + 8 + 2x + -2x2 = -8 + 8 + 4x

Combine like terms: -8 + 8 = 0
0 + 2x + -2x2 = -8 + 8 + 4x
2x + -2x2 = -8 + 8 + 4x

Combine like terms: -8 + 8 = 0
2x + -2x2 = 0 + 4x
2x + -2x2 = 4x

Solving
2x + -2x2 = 4x

Solving for variable 'x'.

Reorder the terms:
2x + -4x + -2x2 = 4x + -4x

Combine like terms: 2x + -4x = -2x
-2x + -2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(1 + x) = 0

Ignore the factor -2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {0, -1}

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