(3x-2)(4-x)-(2x-3)=7-3x

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


Simplifying
(3x + -2)(4 + -1x) + -1(2x + -3) = 7 + -3x

Reorder the terms:
(-2 + 3x)(4 + -1x) + -1(2x + -3) = 7 + -3x

Multiply (-2 + 3x) * (4 + -1x)
(-2(4 + -1x) + 3x * (4 + -1x)) + -1(2x + -3) = 7 + -3x
((4 * -2 + -1x * -2) + 3x * (4 + -1x)) + -1(2x + -3) = 7 + -3x
((-8 + 2x) + 3x * (4 + -1x)) + -1(2x + -3) = 7 + -3x
(-8 + 2x + (4 * 3x + -1x * 3x)) + -1(2x + -3) = 7 + -3x
(-8 + 2x + (12x + -3x2)) + -1(2x + -3) = 7 + -3x

Combine like terms: 2x + 12x = 14x
(-8 + 14x + -3x2) + -1(2x + -3) = 7 + -3x

Reorder the terms:
-8 + 14x + -3x2 + -1(-3 + 2x) = 7 + -3x
-8 + 14x + -3x2 + (-3 * -1 + 2x * -1) = 7 + -3x
-8 + 14x + -3x2 + (3 + -2x) = 7 + -3x

Reorder the terms:
-8 + 3 + 14x + -2x + -3x2 = 7 + -3x

Combine like terms: -8 + 3 = -5
-5 + 14x + -2x + -3x2 = 7 + -3x

Combine like terms: 14x + -2x = 12x
-5 + 12x + -3x2 = 7 + -3x

Solving
-5 + 12x + -3x2 = 7 + -3x

Solving for variable 'x'.

Reorder the terms:
-5 + -7 + 12x + 3x + -3x2 = 7 + -3x + -7 + 3x

Combine like terms: -5 + -7 = -12
-12 + 12x + 3x + -3x2 = 7 + -3x + -7 + 3x

Combine like terms: 12x + 3x = 15x
-12 + 15x + -3x2 = 7 + -3x + -7 + 3x

Reorder the terms:
-12 + 15x + -3x2 = 7 + -7 + -3x + 3x

Combine like terms: 7 + -7 = 0
-12 + 15x + -3x2 = 0 + -3x + 3x
-12 + 15x + -3x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-12 + 15x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 5x + -1x2) = 0

Factor a trinomial.
3((-4 + x)(1 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

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

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

Subproblem 2
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
Solution
x = {4, 1}

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