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

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


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

Reorder the terms:
7(-4 + x) = 2x(x + -4) + -3(x + -4)
(-4 * 7 + x * 7) = 2x(x + -4) + -3(x + -4)
(-28 + 7x) = 2x(x + -4) + -3(x + -4)

Reorder the terms:
-28 + 7x = 2x(-4 + x) + -3(x + -4)
-28 + 7x = (-4 * 2x + x * 2x) + -3(x + -4)
-28 + 7x = (-8x + 2x2) + -3(x + -4)

Reorder the terms:
-28 + 7x = -8x + 2x2 + -3(-4 + x)
-28 + 7x = -8x + 2x2 + (-4 * -3 + x * -3)
-28 + 7x = -8x + 2x2 + (12 + -3x)

Reorder the terms:
-28 + 7x = 12 + -8x + -3x + 2x2

Combine like terms: -8x + -3x = -11x
-28 + 7x = 12 + -11x + 2x2

Solving
-28 + 7x = 12 + -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
-28 + -12 + 7x + 11x + -2x2 = 12 + -11x + 2x2 + -12 + 11x + -2x2

Combine like terms: -28 + -12 = -40
-40 + 7x + 11x + -2x2 = 12 + -11x + 2x2 + -12 + 11x + -2x2

Combine like terms: 7x + 11x = 18x
-40 + 18x + -2x2 = 12 + -11x + 2x2 + -12 + 11x + -2x2

Reorder the terms:
-40 + 18x + -2x2 = 12 + -12 + -11x + 11x + 2x2 + -2x2

Combine like terms: 12 + -12 = 0
-40 + 18x + -2x2 = 0 + -11x + 11x + 2x2 + -2x2
-40 + 18x + -2x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
-40 + 18x + -2x2 = 0 + 2x2 + -2x2
-40 + 18x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-40 + 18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 9x + -1x2) = 0

Factor a trinomial.
2((-5 + x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

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

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

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

Simplifying
x = 5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {5, 4}

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