-(x^2+49+14x)=-7x(x+1)

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Solution for -(x^2+49+14x)=-7x(x+1) equation: 


Simplifying
-1(x2 + 49 + 14x) = -7x(x + 1)

Reorder the terms:
-1(49 + 14x + x2) = -7x(x + 1)
(49 * -1 + 14x * -1 + x2 * -1) = -7x(x + 1)
(-49 + -14x + -1x2) = -7x(x + 1)

Reorder the terms:
-49 + -14x + -1x2 = -7x(1 + x)
-49 + -14x + -1x2 = (1 * -7x + x * -7x)
-49 + -14x + -1x2 = (-7x + -7x2)

Solving
-49 + -14x + -1x2 = -7x + -7x2

Solving for variable 'x'.

Reorder the terms:
-49 + -14x + 7x + -1x2 + 7x2 = -7x + -7x2 + 7x + 7x2

Combine like terms: -14x + 7x = -7x
-49 + -7x + -1x2 + 7x2 = -7x + -7x2 + 7x + 7x2

Combine like terms: -1x2 + 7x2 = 6x2
-49 + -7x + 6x2 = -7x + -7x2 + 7x + 7x2

Reorder the terms:
-49 + -7x + 6x2 = -7x + 7x + -7x2 + 7x2

Combine like terms: -7x + 7x = 0
-49 + -7x + 6x2 = 0 + -7x2 + 7x2
-49 + -7x + 6x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-49 + -7x + 6x2 = 0

Factor a trinomial.
(-7 + -3x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-2.333333333, 3.5}

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