4x^2+5x=2x^2-7x-16

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Solution for 4x^2+5x=2x^2-7x-16 equation: 


Simplifying
4x2 + 5x = 2x2 + -7x + -16

Reorder the terms:
5x + 4x2 = 2x2 + -7x + -16

Reorder the terms:
5x + 4x2 = -16 + -7x + 2x2

Solving
5x + 4x2 = -16 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
16 + 5x + 7x + 4x2 + -2x2 = -16 + -7x + 2x2 + 16 + 7x + -2x2

Combine like terms: 5x + 7x = 12x
16 + 12x + 4x2 + -2x2 = -16 + -7x + 2x2 + 16 + 7x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
16 + 12x + 2x2 = -16 + -7x + 2x2 + 16 + 7x + -2x2

Reorder the terms:
16 + 12x + 2x2 = -16 + 16 + -7x + 7x + 2x2 + -2x2

Combine like terms: -16 + 16 = 0
16 + 12x + 2x2 = 0 + -7x + 7x + 2x2 + -2x2
16 + 12x + 2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
16 + 12x + 2x2 = 0 + 2x2 + -2x2
16 + 12x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
16 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 6x + x2) = 0

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

Ignore the factor 2.

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {-4, -2}

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