x-1(x+5)=2x(2x+6)

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Solution for x-1(x+5)=2x(2x+6) equation: 


Simplifying
x + -1(x + 5) = 2x(2x + 6)

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

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

Combine like terms: x + -1x = 0
-5 + 0 = 2x(2x + 6)
-5 = 2x(2x + 6)

Reorder the terms:
-5 = 2x(6 + 2x)
-5 = (6 * 2x + 2x * 2x)
-5 = (12x + 4x2)

Solving
-5 = 12x + 4x2

Solving for variable 'x'.

Reorder the terms:
-5 + -12x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
-5 + -12x + -4x2 = 0 + 4x2 + -4x2
-5 + -12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + -12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 12x + 4x2) = 0

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

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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

Simplifying
1 + 2x = 0

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

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2.5, -0.5}

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