7x^2+7x-11=45-34x

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Solution for 7x^2+7x-11=45-34x equation: 


Simplifying
7x2 + 7x + -11 = 45 + -34x

Reorder the terms:
-11 + 7x + 7x2 = 45 + -34x

Solving
-11 + 7x + 7x2 = 45 + -34x

Solving for variable 'x'.

Reorder the terms:
-11 + -45 + 7x + 34x + 7x2 = 45 + -34x + -45 + 34x

Combine like terms: -11 + -45 = -56
-56 + 7x + 34x + 7x2 = 45 + -34x + -45 + 34x

Combine like terms: 7x + 34x = 41x
-56 + 41x + 7x2 = 45 + -34x + -45 + 34x

Reorder the terms:
-56 + 41x + 7x2 = 45 + -45 + -34x + 34x

Combine like terms: 45 + -45 = 0
-56 + 41x + 7x2 = 0 + -34x + 34x
-56 + 41x + 7x2 = -34x + 34x

Combine like terms: -34x + 34x = 0
-56 + 41x + 7x2 = 0

Factor a trinomial.
(-7 + -1x)(8 + -7x) = 0


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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143
Solution
x = {-7, 1.142857143}

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