7x^2+23x-22=18-4x

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Solution for 7x^2+23x-22=18-4x equation: 


Simplifying
7x2 + 23x + -22 = 18 + -4x

Reorder the terms:
-22 + 23x + 7x2 = 18 + -4x

Solving
-22 + 23x + 7x2 = 18 + -4x

Solving for variable 'x'.

Reorder the terms:
-22 + -18 + 23x + 4x + 7x2 = 18 + -4x + -18 + 4x

Combine like terms: -22 + -18 = -40
-40 + 23x + 4x + 7x2 = 18 + -4x + -18 + 4x

Combine like terms: 23x + 4x = 27x
-40 + 27x + 7x2 = 18 + -4x + -18 + 4x

Reorder the terms:
-40 + 27x + 7x2 = 18 + -18 + -4x + 4x

Combine like terms: 18 + -18 = 0
-40 + 27x + 7x2 = 0 + -4x + 4x
-40 + 27x + 7x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-40 + 27x + 7x2 = 0

Factor a trinomial.
(-5 + -1x)(8 + -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 '(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 = {-5, 1.142857143}

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