5*8=(x-4)*[(x-4)+(x-2)]

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Solution for 5*8=(x-4)*[(x-4)+(x-2)] equation:


Simplifying
5 * 8 = (x + -4)[(x + -4) + (x + -2)]

Multiply 5 * 8
40 = (x + -4)[(x + -4) + (x + -2)]

Reorder the terms:
40 = (-4 + x)[(x + -4) + (x + -2)]

Reorder the terms:
40 = (-4 + x)[(-4 + x) + (x + -2)]

Remove parenthesis around (-4 + x)
40 = (-4 + x)[-4 + x + (x + -2)]

Reorder the terms:
40 = (-4 + x)[-4 + x + (-2 + x)]

Remove parenthesis around (-2 + x)
40 = (-4 + x)[-4 + x + -2 + x]

Reorder the terms:
40 = (-4 + x)[-4 + -2 + x + x]

Combine like terms: -4 + -2 = -6
40 = (-4 + x)[-6 + x + x]

Combine like terms: x + x = 2x
40 = (-4 + x)[-6 + 2x]

Multiply (-4 + x) * [-6 + 2x]
40 = (-4[-6 + 2x] + x[-6 + 2x])
40 = ([-6 * -4 + 2x * -4] + x[-6 + 2x])
40 = ([24 + -8x] + x[-6 + 2x])
40 = (24 + -8x + [-6 * x + 2x * x])
40 = (24 + -8x + [-6x + 2x2])

Combine like terms: -8x + -6x = -14x
40 = (24 + -14x + 2x2)

Solving
40 = 24 + -14x + 2x2

Solving for variable 'x'.

Combine like terms: 40 + -24 = 16
16 + 14x + -2x2 = 24 + -14x + 2x2 + -24 + 14x + -2x2

Reorder the terms:
16 + 14x + -2x2 = 24 + -24 + -14x + 14x + 2x2 + -2x2

Combine like terms: 24 + -24 = 0
16 + 14x + -2x2 = 0 + -14x + 14x + 2x2 + -2x2
16 + 14x + -2x2 = -14x + 14x + 2x2 + -2x2

Combine like terms: -14x + 14x = 0
16 + 14x + -2x2 = 0 + 2x2 + -2x2
16 + 14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
16 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 7x + -1x2) = 0

Factor a trinomial.
2((8 + -1x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

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 = {8, -1}

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