4x^2+5x-14=31-26x

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Solution for 4x^2+5x-14=31-26x equation: 


Simplifying
4x2 + 5x + -14 = 31 + -26x

Reorder the terms:
-14 + 5x + 4x2 = 31 + -26x

Solving
-14 + 5x + 4x2 = 31 + -26x

Solving for variable 'x'.

Reorder the terms:
-14 + -31 + 5x + 26x + 4x2 = 31 + -26x + -31 + 26x

Combine like terms: -14 + -31 = -45
-45 + 5x + 26x + 4x2 = 31 + -26x + -31 + 26x

Combine like terms: 5x + 26x = 31x
-45 + 31x + 4x2 = 31 + -26x + -31 + 26x

Reorder the terms:
-45 + 31x + 4x2 = 31 + -31 + -26x + 26x

Combine like terms: 31 + -31 = 0
-45 + 31x + 4x2 = 0 + -26x + 26x
-45 + 31x + 4x2 = -26x + 26x

Combine like terms: -26x + 26x = 0
-45 + 31x + 4x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -4x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-9, 1.25}

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