7(x^2-7x-7)=67x+2

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Solution for 7(x^2-7x-7)=67x+2 equation:


Simplifying
7(x2 + -7x + -7) = 67x + 2

Reorder the terms:
7(-7 + -7x + x2) = 67x + 2
(-7 * 7 + -7x * 7 + x2 * 7) = 67x + 2
(-49 + -49x + 7x2) = 67x + 2

Reorder the terms:
-49 + -49x + 7x2 = 2 + 67x

Solving
-49 + -49x + 7x2 = 2 + 67x

Solving for variable 'x'.

Reorder the terms:
-49 + -2 + -49x + -67x + 7x2 = 2 + 67x + -2 + -67x

Combine like terms: -49 + -2 = -51
-51 + -49x + -67x + 7x2 = 2 + 67x + -2 + -67x

Combine like terms: -49x + -67x = -116x
-51 + -116x + 7x2 = 2 + 67x + -2 + -67x

Reorder the terms:
-51 + -116x + 7x2 = 2 + -2 + 67x + -67x

Combine like terms: 2 + -2 = 0
-51 + -116x + 7x2 = 0 + 67x + -67x
-51 + -116x + 7x2 = 67x + -67x

Combine like terms: 67x + -67x = 0
-51 + -116x + 7x2 = 0

Factor a trinomial.
(-3 + -7x)(17 + -1x) = 0


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

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 0

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

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

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

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

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-0.4285714286, 17}

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