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

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Solution for 10(x+4)=(x-1)(x+4) equation: 


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

Reorder the terms:
10(4 + x) = (x + -1)(x + 4)
(4 * 10 + x * 10) = (x + -1)(x + 4)
(40 + 10x) = (x + -1)(x + 4)

Reorder the terms:
40 + 10x = (-1 + x)(x + 4)

Reorder the terms:
40 + 10x = (-1 + x)(4 + x)

Multiply (-1 + x) * (4 + x)
40 + 10x = (-1(4 + x) + x(4 + x))
40 + 10x = ((4 * -1 + x * -1) + x(4 + x))
40 + 10x = ((-4 + -1x) + x(4 + x))
40 + 10x = (-4 + -1x + (4 * x + x * x))
40 + 10x = (-4 + -1x + (4x + x2))

Combine like terms: -1x + 4x = 3x
40 + 10x = (-4 + 3x + x2)

Solving
40 + 10x = -4 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
40 + 4 + 10x + -3x + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Combine like terms: 40 + 4 = 44
44 + 10x + -3x + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Combine like terms: 10x + -3x = 7x
44 + 7x + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Reorder the terms:
44 + 7x + -1x2 = -4 + 4 + 3x + -3x + x2 + -1x2

Combine like terms: -4 + 4 = 0
44 + 7x + -1x2 = 0 + 3x + -3x + x2 + -1x2
44 + 7x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
44 + 7x + -1x2 = 0 + x2 + -1x2
44 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
44 + 7x + -1x2 = 0

Factor a trinomial.
(11 + -1x)(4 + x) = 0


Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 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 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11

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

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Solution
x = {11, -4}

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