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

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


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

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

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

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

Combine like terms: 2x + 5x = 7x
-1(5 + 7x + 2x2) = (2x + 3)(x + -4) + 5
(5 * -1 + 7x * -1 + 2x2 * -1) = (2x + 3)(x + -4) + 5
(-5 + -7x + -2x2) = (2x + 3)(x + -4) + 5

Reorder the terms:
-5 + -7x + -2x2 = (3 + 2x)(x + -4) + 5

Reorder the terms:
-5 + -7x + -2x2 = (3 + 2x)(-4 + x) + 5

Multiply (3 + 2x) * (-4 + x)
-5 + -7x + -2x2 = (3(-4 + x) + 2x * (-4 + x)) + 5
-5 + -7x + -2x2 = ((-4 * 3 + x * 3) + 2x * (-4 + x)) + 5
-5 + -7x + -2x2 = ((-12 + 3x) + 2x * (-4 + x)) + 5
-5 + -7x + -2x2 = (-12 + 3x + (-4 * 2x + x * 2x)) + 5
-5 + -7x + -2x2 = (-12 + 3x + (-8x + 2x2)) + 5

Combine like terms: 3x + -8x = -5x
-5 + -7x + -2x2 = (-12 + -5x + 2x2) + 5

Reorder the terms:
-5 + -7x + -2x2 = -12 + 5 + -5x + 2x2

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

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

Solving for variable 'x'.

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

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

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

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

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

Combine like terms: -7 + 7 = 0
2 + -2x + -4x2 = 0 + -5x + 5x + 2x2 + -2x2
2 + -2x + -4x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
2 + -2x + -4x2 = 0 + 2x2 + -2x2
2 + -2x + -4x2 = 2x2 + -2x2

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

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

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0.5, -1}

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