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

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


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

Reorder the terms:
4(-4 + x) + 4(x + -1) = 5(x + -1)(x + -4)
(-4 * 4 + x * 4) + 4(x + -1) = 5(x + -1)(x + -4)
(-16 + 4x) + 4(x + -1) = 5(x + -1)(x + -4)

Reorder the terms:
-16 + 4x + 4(-1 + x) = 5(x + -1)(x + -4)
-16 + 4x + (-1 * 4 + x * 4) = 5(x + -1)(x + -4)
-16 + 4x + (-4 + 4x) = 5(x + -1)(x + -4)

Reorder the terms:
-16 + -4 + 4x + 4x = 5(x + -1)(x + -4)

Combine like terms: -16 + -4 = -20
-20 + 4x + 4x = 5(x + -1)(x + -4)

Combine like terms: 4x + 4x = 8x
-20 + 8x = 5(x + -1)(x + -4)

Reorder the terms:
-20 + 8x = 5(-1 + x)(x + -4)

Reorder the terms:
-20 + 8x = 5(-1 + x)(-4 + x)

Multiply (-1 + x) * (-4 + x)
-20 + 8x = 5(-1(-4 + x) + x(-4 + x))
-20 + 8x = 5((-4 * -1 + x * -1) + x(-4 + x))
-20 + 8x = 5((4 + -1x) + x(-4 + x))
-20 + 8x = 5(4 + -1x + (-4 * x + x * x))
-20 + 8x = 5(4 + -1x + (-4x + x2))

Combine like terms: -1x + -4x = -5x
-20 + 8x = 5(4 + -5x + x2)
-20 + 8x = (4 * 5 + -5x * 5 + x2 * 5)
-20 + 8x = (20 + -25x + 5x2)

Solving
-20 + 8x = 20 + -25x + 5x2

Solving for variable 'x'.

Reorder the terms:
-20 + -20 + 8x + 25x + -5x2 = 20 + -25x + 5x2 + -20 + 25x + -5x2

Combine like terms: -20 + -20 = -40
-40 + 8x + 25x + -5x2 = 20 + -25x + 5x2 + -20 + 25x + -5x2

Combine like terms: 8x + 25x = 33x
-40 + 33x + -5x2 = 20 + -25x + 5x2 + -20 + 25x + -5x2

Reorder the terms:
-40 + 33x + -5x2 = 20 + -20 + -25x + 25x + 5x2 + -5x2

Combine like terms: 20 + -20 = 0
-40 + 33x + -5x2 = 0 + -25x + 25x + 5x2 + -5x2
-40 + 33x + -5x2 = -25x + 25x + 5x2 + -5x2

Combine like terms: -25x + 25x = 0
-40 + 33x + -5x2 = 0 + 5x2 + -5x2
-40 + 33x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-40 + 33x + -5x2 = 0

Factor a trinomial.
(-5 + x)(8 + -5x) = 0

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 '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 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 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6

Solution

x = {5, 1.6}

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