4x^2+4x-5=2x(x+3)-1

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Solution for 4x^2+4x-5=2x(x+3)-1 equation: 


Simplifying
4x2 + 4x + -5 = 2x(x + 3) + -1

Reorder the terms:
-5 + 4x + 4x2 = 2x(x + 3) + -1

Reorder the terms:
-5 + 4x + 4x2 = 2x(3 + x) + -1
-5 + 4x + 4x2 = (3 * 2x + x * 2x) + -1
-5 + 4x + 4x2 = (6x + 2x2) + -1

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

Solving
-5 + 4x + 4x2 = -1 + 6x + 2x2

Solving for variable 'x'.

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

Combine like terms: -5 + 1 = -4
-4 + 4x + -6x + 4x2 + -2x2 = -1 + 6x + 2x2 + 1 + -6x + -2x2

Combine like terms: 4x + -6x = -2x
-4 + -2x + 4x2 + -2x2 = -1 + 6x + 2x2 + 1 + -6x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
-4 + -2x + 2x2 = -1 + 6x + 2x2 + 1 + -6x + -2x2

Reorder the terms:
-4 + -2x + 2x2 = -1 + 1 + 6x + -6x + 2x2 + -2x2

Combine like terms: -1 + 1 = 0
-4 + -2x + 2x2 = 0 + 6x + -6x + 2x2 + -2x2
-4 + -2x + 2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
-4 + -2x + 2x2 = 0 + 2x2 + -2x2
-4 + -2x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + -2x + 2x2 = 0

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

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

Ignore the factor 2.

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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