4x^2-4x-37=3x^2+5-5x

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Solution for 4x^2-4x-37=3x^2+5-5x equation: 


Simplifying
4x2 + -4x + -37 = 3x2 + 5 + -5x

Reorder the terms:
-37 + -4x + 4x2 = 3x2 + 5 + -5x

Reorder the terms:
-37 + -4x + 4x2 = 5 + -5x + 3x2

Solving
-37 + -4x + 4x2 = 5 + -5x + 3x2

Solving for variable 'x'.

Reorder the terms:
-37 + -5 + -4x + 5x + 4x2 + -3x2 = 5 + -5x + 3x2 + -5 + 5x + -3x2

Combine like terms: -37 + -5 = -42
-42 + -4x + 5x + 4x2 + -3x2 = 5 + -5x + 3x2 + -5 + 5x + -3x2

Combine like terms: -4x + 5x = 1x
-42 + 1x + 4x2 + -3x2 = 5 + -5x + 3x2 + -5 + 5x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-42 + 1x + 1x2 = 5 + -5x + 3x2 + -5 + 5x + -3x2

Reorder the terms:
-42 + 1x + 1x2 = 5 + -5 + -5x + 5x + 3x2 + -3x2

Combine like terms: 5 + -5 = 0
-42 + 1x + 1x2 = 0 + -5x + 5x + 3x2 + -3x2
-42 + 1x + 1x2 = -5x + 5x + 3x2 + -3x2

Combine like terms: -5x + 5x = 0
-42 + 1x + 1x2 = 0 + 3x2 + -3x2
-42 + 1x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-42 + 1x + 1x2 = 0

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


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
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
Solution
x = {-7, 6}

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