7x^2+24x-22=8-5x

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Solution for 7x^2+24x-22=8-5x equation: 


Simplifying
7x2 + 24x + -22 = 8 + -5x

Reorder the terms:
-22 + 24x + 7x2 = 8 + -5x

Solving
-22 + 24x + 7x2 = 8 + -5x

Solving for variable 'x'.

Reorder the terms:
-22 + -8 + 24x + 5x + 7x2 = 8 + -5x + -8 + 5x

Combine like terms: -22 + -8 = -30
-30 + 24x + 5x + 7x2 = 8 + -5x + -8 + 5x

Combine like terms: 24x + 5x = 29x
-30 + 29x + 7x2 = 8 + -5x + -8 + 5x

Reorder the terms:
-30 + 29x + 7x2 = 8 + -8 + -5x + 5x

Combine like terms: 8 + -8 = 0
-30 + 29x + 7x2 = 0 + -5x + 5x
-30 + 29x + 7x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-30 + 29x + 7x2 = 0

Factor a trinomial.
(-5 + -1x)(6 + -7x) = 0


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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x = 0 + -6
-7x = 0 + -6

Combine like terms: 0 + -6 = -6
-7x = -6

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
Solution
x = {-5, 0.8571428571}

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