4x^2+16x-19=6-4x-x^2

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Solution for 4x^2+16x-19=6-4x-x^2 equation:


Simplifying
4x2 + 16x + -19 = 6 + -4x + -1x2

Reorder the terms:
-19 + 16x + 4x2 = 6 + -4x + -1x2

Solving
-19 + 16x + 4x2 = 6 + -4x + -1x2

Solving for variable 'x'.

Reorder the terms:
-19 + -6 + 16x + 4x + 4x2 + x2 = 6 + -4x + -1x2 + -6 + 4x + x2

Combine like terms: -19 + -6 = -25
-25 + 16x + 4x + 4x2 + x2 = 6 + -4x + -1x2 + -6 + 4x + x2

Combine like terms: 16x + 4x = 20x
-25 + 20x + 4x2 + x2 = 6 + -4x + -1x2 + -6 + 4x + x2

Combine like terms: 4x2 + x2 = 5x2
-25 + 20x + 5x2 = 6 + -4x + -1x2 + -6 + 4x + x2

Reorder the terms:
-25 + 20x + 5x2 = 6 + -6 + -4x + 4x + -1x2 + x2

Combine like terms: 6 + -6 = 0
-25 + 20x + 5x2 = 0 + -4x + 4x + -1x2 + x2
-25 + 20x + 5x2 = -4x + 4x + -1x2 + x2

Combine like terms: -4x + 4x = 0
-25 + 20x + 5x2 = 0 + -1x2 + x2
-25 + 20x + 5x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-25 + 20x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 4x + x2) = 0

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

Ignore the factor 5.

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

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

Solution

x = {-5, 1}

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