(x-7)(x-7)=20x+49

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Solution for (x-7)(x-7)=20x+49 equation: 


Simplifying
(x + -7)(x + -7) = 20x + 49

Reorder the terms:
(-7 + x)(x + -7) = 20x + 49

Reorder the terms:
(-7 + x)(-7 + x) = 20x + 49

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) = 20x + 49
((-7 * -7 + x * -7) + x(-7 + x)) = 20x + 49
((49 + -7x) + x(-7 + x)) = 20x + 49
(49 + -7x + (-7 * x + x * x)) = 20x + 49
(49 + -7x + (-7x + x2)) = 20x + 49

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) = 20x + 49

Reorder the terms:
49 + -14x + x2 = 49 + 20x

Add '-49' to each side of the equation.
49 + -14x + -49 + x2 = 49 + -49 + 20x

Reorder the terms:
49 + -49 + -14x + x2 = 49 + -49 + 20x

Combine like terms: 49 + -49 = 0
0 + -14x + x2 = 49 + -49 + 20x
-14x + x2 = 49 + -49 + 20x

Combine like terms: 49 + -49 = 0
-14x + x2 = 0 + 20x
-14x + x2 = 20x

Solving
-14x + x2 = 20x

Solving for variable 'x'.

Reorder the terms:
-14x + -20x + x2 = 20x + -20x

Combine like terms: -14x + -20x = -34x
-34x + x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
-34x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-34 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-34 + x)' equal to zero and attempt to solve:

Simplifying
-34 + x = 0

Solving
-34 + x = 0

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

Add '34' to each side of the equation.
-34 + 34 + x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + x = 0 + 34
x = 0 + 34

Combine like terms: 0 + 34 = 34
x = 34

Simplifying
x = 34
Solution
x = {0, 34}

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