(4x+5)4=(x+5)(x+5)

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


Simplifying
(4x + 5) * 4 = (x + 5)(x + 5)

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

Reorder the terms for easier multiplication:
4(5 + 4x) = (x + 5)(x + 5)
(5 * 4 + 4x * 4) = (x + 5)(x + 5)
(20 + 16x) = (x + 5)(x + 5)

Reorder the terms:
20 + 16x = (5 + x)(x + 5)

Reorder the terms:
20 + 16x = (5 + x)(5 + x)

Multiply (5 + x) * (5 + x)
20 + 16x = (5(5 + x) + x(5 + x))
20 + 16x = ((5 * 5 + x * 5) + x(5 + x))
20 + 16x = ((25 + 5x) + x(5 + x))
20 + 16x = (25 + 5x + (5 * x + x * x))
20 + 16x = (25 + 5x + (5x + x2))

Combine like terms: 5x + 5x = 10x
20 + 16x = (25 + 10x + x2)

Solving
20 + 16x = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
20 + -25 + 16x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 20 + -25 = -5
-5 + 16x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 16x + -10x = 6x
-5 + 6x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
-5 + 6x + -1x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-5 + 6x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-5 + 6x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-5 + 6x + -1x2 = 0 + x2 + -1x2
-5 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + 6x + -1x2 = 0

Factor a trinomial.
(-5 + x)(1 + -1x) = 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 '(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 = {5, 1}

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