25(x^2+4x+4)+81=x^2-14x+49

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Solution for 25(x^2+4x+4)+81=x^2-14x+49 equation: 


Simplifying
25(x2 + 4x + 4) + 81 = x2 + -14x + 49

Reorder the terms:
25(4 + 4x + x2) + 81 = x2 + -14x + 49
(4 * 25 + 4x * 25 + x2 * 25) + 81 = x2 + -14x + 49
(100 + 100x + 25x2) + 81 = x2 + -14x + 49

Reorder the terms:
100 + 81 + 100x + 25x2 = x2 + -14x + 49

Combine like terms: 100 + 81 = 181
181 + 100x + 25x2 = x2 + -14x + 49

Reorder the terms:
181 + 100x + 25x2 = 49 + -14x + x2

Solving
181 + 100x + 25x2 = 49 + -14x + x2

Solving for variable 'x'.

Reorder the terms:
181 + -49 + 100x + 14x + 25x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 181 + -49 = 132
132 + 100x + 14x + 25x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 100x + 14x = 114x
132 + 114x + 25x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 25x2 + -1x2 = 24x2
132 + 114x + 24x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Reorder the terms:
132 + 114x + 24x2 = 49 + -49 + -14x + 14x + x2 + -1x2

Combine like terms: 49 + -49 = 0
132 + 114x + 24x2 = 0 + -14x + 14x + x2 + -1x2
132 + 114x + 24x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
132 + 114x + 24x2 = 0 + x2 + -1x2
132 + 114x + 24x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
132 + 114x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(22 + 19x + 4x2) = 0

Factor a trinomial.
6((11 + 4x)(2 + x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(11 + 4x)' equal to zero and attempt to solve:

Simplifying
11 + 4x = 0

Solving
11 + 4x = 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 + 4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 4x = 0 + -11
4x = 0 + -11

Combine like terms: 0 + -11 = -11
4x = -11

Divide each side by '4'.
x = -2.75

Simplifying
x = -2.75

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {-2.75, -2}

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