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

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


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

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

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

Multiply (-4 + x) * (-4 + x)
(-4(-4 + x) + x(-4 + x)) = (x + -4)(2x + -1)
((-4 * -4 + x * -4) + x(-4 + x)) = (x + -4)(2x + -1)
((16 + -4x) + x(-4 + x)) = (x + -4)(2x + -1)
(16 + -4x + (-4 * x + x * x)) = (x + -4)(2x + -1)
(16 + -4x + (-4x + x2)) = (x + -4)(2x + -1)

Combine like terms: -4x + -4x = -8x
(16 + -8x + x2) = (x + -4)(2x + -1)

Reorder the terms:
16 + -8x + x2 = (-4 + x)(2x + -1)

Reorder the terms:
16 + -8x + x2 = (-4 + x)(-1 + 2x)

Multiply (-4 + x) * (-1 + 2x)
16 + -8x + x2 = (-4(-1 + 2x) + x(-1 + 2x))
16 + -8x + x2 = ((-1 * -4 + 2x * -4) + x(-1 + 2x))
16 + -8x + x2 = ((4 + -8x) + x(-1 + 2x))
16 + -8x + x2 = (4 + -8x + (-1 * x + 2x * x))
16 + -8x + x2 = (4 + -8x + (-1x + 2x2))

Combine like terms: -8x + -1x = -9x
16 + -8x + x2 = (4 + -9x + 2x2)

Solving
16 + -8x + x2 = 4 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
16 + -4 + -8x + 9x + x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Combine like terms: 16 + -4 = 12
12 + -8x + 9x + x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Combine like terms: -8x + 9x = 1x
12 + 1x + x2 + -2x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Combine like terms: x2 + -2x2 = -1x2
12 + 1x + -1x2 = 4 + -9x + 2x2 + -4 + 9x + -2x2

Reorder the terms:
12 + 1x + -1x2 = 4 + -4 + -9x + 9x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
12 + 1x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2
12 + 1x + -1x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
12 + 1x + -1x2 = 0 + 2x2 + -2x2
12 + 1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + 1x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(3 + x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {4, -3}

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