7x^2+3x-11=53-45x

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Solution for 7x^2+3x-11=53-45x equation: 


Simplifying
7x2 + 3x + -11 = 53 + -45x

Reorder the terms:
-11 + 3x + 7x2 = 53 + -45x

Solving
-11 + 3x + 7x2 = 53 + -45x

Solving for variable 'x'.

Reorder the terms:
-11 + -53 + 3x + 45x + 7x2 = 53 + -45x + -53 + 45x

Combine like terms: -11 + -53 = -64
-64 + 3x + 45x + 7x2 = 53 + -45x + -53 + 45x

Combine like terms: 3x + 45x = 48x
-64 + 48x + 7x2 = 53 + -45x + -53 + 45x

Reorder the terms:
-64 + 48x + 7x2 = 53 + -53 + -45x + 45x

Combine like terms: 53 + -53 = 0
-64 + 48x + 7x2 = 0 + -45x + 45x
-64 + 48x + 7x2 = -45x + 45x

Combine like terms: -45x + 45x = 0
-64 + 48x + 7x2 = 0

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


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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 = {-8, 1.142857143}

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