5(x-1)=4(x-1)2(x+2)

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Solution for 5(x-1)=4(x-1)2(x+2) equation: 


Simplifying
5(x + -1) = 4(x + -1) * 2(x + 2)

Reorder the terms:
5(-1 + x) = 4(x + -1) * 2(x + 2)
(-1 * 5 + x * 5) = 4(x + -1) * 2(x + 2)
(-5 + 5x) = 4(x + -1) * 2(x + 2)

Reorder the terms:
-5 + 5x = 4(-1 + x) * 2(x + 2)

Reorder the terms:
-5 + 5x = 4(-1 + x) * 2(2 + x)

Reorder the terms for easier multiplication:
-5 + 5x = 4 * 2(-1 + x)(2 + x)

Multiply 4 * 2
-5 + 5x = 8(-1 + x)(2 + x)

Multiply (-1 + x) * (2 + x)
-5 + 5x = 8(-1(2 + x) + x(2 + x))
-5 + 5x = 8((2 * -1 + x * -1) + x(2 + x))
-5 + 5x = 8((-2 + -1x) + x(2 + x))
-5 + 5x = 8(-2 + -1x + (2 * x + x * x))
-5 + 5x = 8(-2 + -1x + (2x + x2))

Combine like terms: -1x + 2x = 1x
-5 + 5x = 8(-2 + 1x + x2)
-5 + 5x = (-2 * 8 + 1x * 8 + x2 * 8)
-5 + 5x = (-16 + 8x + 8x2)

Solving
-5 + 5x = -16 + 8x + 8x2

Solving for variable 'x'.

Reorder the terms:
-5 + 16 + 5x + -8x + -8x2 = -16 + 8x + 8x2 + 16 + -8x + -8x2

Combine like terms: -5 + 16 = 11
11 + 5x + -8x + -8x2 = -16 + 8x + 8x2 + 16 + -8x + -8x2

Combine like terms: 5x + -8x = -3x
11 + -3x + -8x2 = -16 + 8x + 8x2 + 16 + -8x + -8x2

Reorder the terms:
11 + -3x + -8x2 = -16 + 16 + 8x + -8x + 8x2 + -8x2

Combine like terms: -16 + 16 = 0
11 + -3x + -8x2 = 0 + 8x + -8x + 8x2 + -8x2
11 + -3x + -8x2 = 8x + -8x + 8x2 + -8x2

Combine like terms: 8x + -8x = 0
11 + -3x + -8x2 = 0 + 8x2 + -8x2
11 + -3x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
11 + -3x + -8x2 = 0

Factor a trinomial.
(1 + -1x)(11 + 8x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(11 + 8x)' equal to zero and attempt to solve:

Simplifying
11 + 8x = 0

Solving
11 + 8x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 8x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 8x = 0 + -11
8x = 0 + -11

Combine like terms: 0 + -11 = -11
8x = -11

Divide each side by '8'.
x = -1.375

Simplifying
x = -1.375
Solution
x = {1, -1.375}

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