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

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


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

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

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

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

Multiply (-7 + x) * (-7 + x)
1 + 2x = (-7(-7 + x) + x(-7 + x))
1 + 2x = ((-7 * -7 + x * -7) + x(-7 + x))
1 + 2x = ((49 + -7x) + x(-7 + x))
1 + 2x = (49 + -7x + (-7 * x + x * x))
1 + 2x = (49 + -7x + (-7x + x2))

Combine like terms: -7x + -7x = -14x
1 + 2x = (49 + -14x + x2)

Solving
1 + 2x = 49 + -14x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -49 + 2x + 14x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 1 + -49 = -48
-48 + 2x + 14x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 2x + 14x = 16x
-48 + 16x + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Reorder the terms:
-48 + 16x + -1x2 = 49 + -49 + -14x + 14x + x2 + -1x2

Combine like terms: 49 + -49 = 0
-48 + 16x + -1x2 = 0 + -14x + 14x + x2 + -1x2
-48 + 16x + -1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
-48 + 16x + -1x2 = 0 + x2 + -1x2
-48 + 16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-48 + 16x + -1x2 = 0

Factor a trinomial.
(-12 + x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve:

Simplifying
-12 + x = 0

Solving
-12 + x = 0

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + x = 0 + 12
x = 0 + 12

Combine like terms: 0 + 12 = 12
x = 12

Simplifying
x = 12

Subproblem 2
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
Solution
x = {12, 4}

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