(2x+4)(2x-4)-(-x^2+5x-6)=

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Solution for (2x+4)(2x-4)-(-x^2+5x-6)= equation: 


Simplifying
(2x + 4)(2x + -4) + -1(-1x2 + 5x + -6) = 0

Reorder the terms:
(4 + 2x)(2x + -4) + -1(-1x2 + 5x + -6) = 0

Reorder the terms:
(4 + 2x)(-4 + 2x) + -1(-1x2 + 5x + -6) = 0

Multiply (4 + 2x) * (-4 + 2x)
(4(-4 + 2x) + 2x * (-4 + 2x)) + -1(-1x2 + 5x + -6) = 0
((-4 * 4 + 2x * 4) + 2x * (-4 + 2x)) + -1(-1x2 + 5x + -6) = 0
((-16 + 8x) + 2x * (-4 + 2x)) + -1(-1x2 + 5x + -6) = 0
(-16 + 8x + (-4 * 2x + 2x * 2x)) + -1(-1x2 + 5x + -6) = 0
(-16 + 8x + (-8x + 4x2)) + -1(-1x2 + 5x + -6) = 0

Combine like terms: 8x + -8x = 0
(-16 + 0 + 4x2) + -1(-1x2 + 5x + -6) = 0
(-16 + 4x2) + -1(-1x2 + 5x + -6) = 0

Reorder the terms:
-16 + 4x2 + -1(-6 + 5x + -1x2) = 0
-16 + 4x2 + (-6 * -1 + 5x * -1 + -1x2 * -1) = 0
-16 + 4x2 + (6 + -5x + 1x2) = 0

Reorder the terms:
-16 + 6 + -5x + 4x2 + 1x2 = 0

Combine like terms: -16 + 6 = -10
-10 + -5x + 4x2 + 1x2 = 0

Combine like terms: 4x2 + 1x2 = 5x2
-10 + -5x + 5x2 = 0

Solving
-10 + -5x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + -1x + x2) = 0

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

Ignore the factor 5.

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}

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