9x^2+x=4x^2-37x+16

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Solution for 9x^2+x=4x^2-37x+16 equation: 


Simplifying
9x2 + x = 4x2 + -37x + 16

Reorder the terms:
x + 9x2 = 4x2 + -37x + 16

Reorder the terms:
x + 9x2 = 16 + -37x + 4x2

Solving
x + 9x2 = 16 + -37x + 4x2

Solving for variable 'x'.

Reorder the terms:
-16 + x + 37x + 9x2 + -4x2 = 16 + -37x + 4x2 + -16 + 37x + -4x2

Combine like terms: x + 37x = 38x
-16 + 38x + 9x2 + -4x2 = 16 + -37x + 4x2 + -16 + 37x + -4x2

Combine like terms: 9x2 + -4x2 = 5x2
-16 + 38x + 5x2 = 16 + -37x + 4x2 + -16 + 37x + -4x2

Reorder the terms:
-16 + 38x + 5x2 = 16 + -16 + -37x + 37x + 4x2 + -4x2

Combine like terms: 16 + -16 = 0
-16 + 38x + 5x2 = 0 + -37x + 37x + 4x2 + -4x2
-16 + 38x + 5x2 = -37x + 37x + 4x2 + -4x2

Combine like terms: -37x + 37x = 0
-16 + 38x + 5x2 = 0 + 4x2 + -4x2
-16 + 38x + 5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-16 + 38x + 5x2 = 0

Factor a trinomial.
(-8 + -1x)(2 + -5x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-8, 0.4}

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