-2x^2-11x+47=-3x^2+3x+7

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Solution for -2x^2-11x+47=-3x^2+3x+7 equation: 


Simplifying
-2x2 + -11x + 47 = -3x2 + 3x + 7

Reorder the terms:
47 + -11x + -2x2 = -3x2 + 3x + 7

Reorder the terms:
47 + -11x + -2x2 = 7 + 3x + -3x2

Solving
47 + -11x + -2x2 = 7 + 3x + -3x2

Solving for variable 'x'.

Reorder the terms:
47 + -7 + -11x + -3x + -2x2 + 3x2 = 7 + 3x + -3x2 + -7 + -3x + 3x2

Combine like terms: 47 + -7 = 40
40 + -11x + -3x + -2x2 + 3x2 = 7 + 3x + -3x2 + -7 + -3x + 3x2

Combine like terms: -11x + -3x = -14x
40 + -14x + -2x2 + 3x2 = 7 + 3x + -3x2 + -7 + -3x + 3x2

Combine like terms: -2x2 + 3x2 = 1x2
40 + -14x + 1x2 = 7 + 3x + -3x2 + -7 + -3x + 3x2

Reorder the terms:
40 + -14x + 1x2 = 7 + -7 + 3x + -3x + -3x2 + 3x2

Combine like terms: 7 + -7 = 0
40 + -14x + 1x2 = 0 + 3x + -3x + -3x2 + 3x2
40 + -14x + 1x2 = 3x + -3x + -3x2 + 3x2

Combine like terms: 3x + -3x = 0
40 + -14x + 1x2 = 0 + -3x2 + 3x2
40 + -14x + 1x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
40 + -14x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {4, 10}

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