7x(x)+4x-17=31-30x

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Solution for 7x(x)+4x-17=31-30x equation: 


Simplifying
7x(x) + 4x + -17 = 31 + -30x

Multiply x * x
7x2 + 4x + -17 = 31 + -30x

Reorder the terms:
-17 + 4x + 7x2 = 31 + -30x

Solving
-17 + 4x + 7x2 = 31 + -30x

Solving for variable 'x'.

Reorder the terms:
-17 + -31 + 4x + 30x + 7x2 = 31 + -30x + -31 + 30x

Combine like terms: -17 + -31 = -48
-48 + 4x + 30x + 7x2 = 31 + -30x + -31 + 30x

Combine like terms: 4x + 30x = 34x
-48 + 34x + 7x2 = 31 + -30x + -31 + 30x

Reorder the terms:
-48 + 34x + 7x2 = 31 + -31 + -30x + 30x

Combine like terms: 31 + -31 = 0
-48 + 34x + 7x2 = 0 + -30x + 30x
-48 + 34x + 7x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
-48 + 34x + 7x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -7x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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 = {-6, 1.142857143}

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