7x^2+32=7-40x

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Solution for 7x^2+32=7-40x equation: 


Simplifying
7x2 + 32 = 7 + -40x

Reorder the terms:
32 + 7x2 = 7 + -40x

Solving
32 + 7x2 = 7 + -40x

Solving for variable 'x'.

Reorder the terms:
32 + -7 + 40x + 7x2 = 7 + -40x + -7 + 40x

Combine like terms: 32 + -7 = 25
25 + 40x + 7x2 = 7 + -40x + -7 + 40x

Reorder the terms:
25 + 40x + 7x2 = 7 + -7 + -40x + 40x

Combine like terms: 7 + -7 = 0
25 + 40x + 7x2 = 0 + -40x + 40x
25 + 40x + 7x2 = -40x + 40x

Combine like terms: -40x + 40x = 0
25 + 40x + 7x2 = 0

Factor a trinomial.
(5 + x)(5 + 7x) = 0


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(5 + 7x)' equal to zero and attempt to solve:

Simplifying
5 + 7x = 0

Solving
5 + 7x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 7x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7x = 0 + -5
7x = 0 + -5

Combine like terms: 0 + -5 = -5
7x = -5

Divide each side by '7'.
x = -0.7142857143

Simplifying
x = -0.7142857143
Solution
x = {-5, -0.7142857143}

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