7x^2+3x-11=61-52x

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Solution for 7x^2+3x-11=61-52x equation: 


Simplifying
7x2 + 3x + -11 = 61 + -52x

Reorder the terms:
-11 + 3x + 7x2 = 61 + -52x

Solving
-11 + 3x + 7x2 = 61 + -52x

Solving for variable 'x'.

Reorder the terms:
-11 + -61 + 3x + 52x + 7x2 = 61 + -52x + -61 + 52x

Combine like terms: -11 + -61 = -72
-72 + 3x + 52x + 7x2 = 61 + -52x + -61 + 52x

Combine like terms: 3x + 52x = 55x
-72 + 55x + 7x2 = 61 + -52x + -61 + 52x

Reorder the terms:
-72 + 55x + 7x2 = 61 + -61 + -52x + 52x

Combine like terms: 61 + -61 = 0
-72 + 55x + 7x2 = 0 + -52x + 52x
-72 + 55x + 7x2 = -52x + 52x

Combine like terms: -52x + 52x = 0
-72 + 55x + 7x2 = 0

Factor a trinomial.
(-9 + -1x)(8 + -7x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 1.142857143}

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