-x^2+6x+11=-5x^2+6x+3-3x(-2x+2)

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Solution for -x^2+6x+11=-5x^2+6x+3-3x(-2x+2) equation:


Simplifying
-1x2 + 6x + 11 = -5x2 + 6x + 3 + -3x(-2x + 2)

Reorder the terms:
11 + 6x + -1x2 = -5x2 + 6x + 3 + -3x(-2x + 2)

Reorder the terms:
11 + 6x + -1x2 = -5x2 + 6x + 3 + -3x(2 + -2x)
11 + 6x + -1x2 = -5x2 + 6x + 3 + (2 * -3x + -2x * -3x)
11 + 6x + -1x2 = -5x2 + 6x + 3 + (-6x + 6x2)

Reorder the terms:
11 + 6x + -1x2 = 3 + 6x + -6x + -5x2 + 6x2

Combine like terms: 6x + -6x = 0
11 + 6x + -1x2 = 3 + 0 + -5x2 + 6x2
11 + 6x + -1x2 = 3 + -5x2 + 6x2

Combine like terms: -5x2 + 6x2 = 1x2
11 + 6x + -1x2 = 3 + 1x2

Solving
11 + 6x + -1x2 = 3 + 1x2

Solving for variable 'x'.

Reorder the terms:
11 + -3 + 6x + -1x2 + -1x2 = 3 + 1x2 + -3 + -1x2

Combine like terms: 11 + -3 = 8
8 + 6x + -1x2 + -1x2 = 3 + 1x2 + -3 + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
8 + 6x + -2x2 = 3 + 1x2 + -3 + -1x2

Reorder the terms:
8 + 6x + -2x2 = 3 + -3 + 1x2 + -1x2

Combine like terms: 3 + -3 = 0
8 + 6x + -2x2 = 0 + 1x2 + -1x2
8 + 6x + -2x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
8 + 6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 3x + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(1 + x)) = 0

Ignore the factor 2.

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {4, -1}

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