-x(x+7)=(x-2)(x+2)

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Solution for -x(x+7)=(x-2)(x+2) equation: 


Simplifying
-1x(x + 7) = (x + -2)(x + 2)

Reorder the terms:
-1x(7 + x) = (x + -2)(x + 2)
(7 * -1x + x * -1x) = (x + -2)(x + 2)
(-7x + -1x2) = (x + -2)(x + 2)

Reorder the terms:
-7x + -1x2 = (-2 + x)(x + 2)

Reorder the terms:
-7x + -1x2 = (-2 + x)(2 + x)

Multiply (-2 + x) * (2 + x)
-7x + -1x2 = (-2(2 + x) + x(2 + x))
-7x + -1x2 = ((2 * -2 + x * -2) + x(2 + x))
-7x + -1x2 = ((-4 + -2x) + x(2 + x))
-7x + -1x2 = (-4 + -2x + (2 * x + x * x))
-7x + -1x2 = (-4 + -2x + (2x + x2))

Combine like terms: -2x + 2x = 0
-7x + -1x2 = (-4 + 0 + x2)
-7x + -1x2 = (-4 + x2)

Solving
-7x + -1x2 = -4 + x2

Solving for variable 'x'.

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

Combine like terms: -1x2 + -1x2 = -2x2
4 + -7x + -2x2 = -4 + x2 + 4 + -1x2

Reorder the terms:
4 + -7x + -2x2 = -4 + 4 + x2 + -1x2

Combine like terms: -4 + 4 = 0
4 + -7x + -2x2 = 0 + x2 + -1x2
4 + -7x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -7x + -2x2 = 0

Factor a trinomial.
(1 + -2x)(4 + x) = 0


Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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 = {0.5, -4}

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