(x+5)(x-9)=(2x+7)(x-5)

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Solution for (x+5)(x-9)=(2x+7)(x-5) equation: 


Simplifying
(x + 5)(x + -9) = (2x + 7)(x + -5)

Reorder the terms:
(5 + x)(x + -9) = (2x + 7)(x + -5)

Reorder the terms:
(5 + x)(-9 + x) = (2x + 7)(x + -5)

Multiply (5 + x) * (-9 + x)
(5(-9 + x) + x(-9 + x)) = (2x + 7)(x + -5)
((-9 * 5 + x * 5) + x(-9 + x)) = (2x + 7)(x + -5)
((-45 + 5x) + x(-9 + x)) = (2x + 7)(x + -5)
(-45 + 5x + (-9 * x + x * x)) = (2x + 7)(x + -5)
(-45 + 5x + (-9x + x2)) = (2x + 7)(x + -5)

Combine like terms: 5x + -9x = -4x
(-45 + -4x + x2) = (2x + 7)(x + -5)

Reorder the terms:
-45 + -4x + x2 = (7 + 2x)(x + -5)

Reorder the terms:
-45 + -4x + x2 = (7 + 2x)(-5 + x)

Multiply (7 + 2x) * (-5 + x)
-45 + -4x + x2 = (7(-5 + x) + 2x * (-5 + x))
-45 + -4x + x2 = ((-5 * 7 + x * 7) + 2x * (-5 + x))
-45 + -4x + x2 = ((-35 + 7x) + 2x * (-5 + x))
-45 + -4x + x2 = (-35 + 7x + (-5 * 2x + x * 2x))
-45 + -4x + x2 = (-35 + 7x + (-10x + 2x2))

Combine like terms: 7x + -10x = -3x
-45 + -4x + x2 = (-35 + -3x + 2x2)

Solving
-45 + -4x + x2 = -35 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-45 + 35 + -4x + 3x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: -45 + 35 = -10
-10 + -4x + 3x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: -4x + 3x = -1x
-10 + -1x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-10 + -1x + -1x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Reorder the terms:
-10 + -1x + -1x2 = -35 + 35 + -3x + 3x + 2x2 + -2x2

Combine like terms: -35 + 35 = 0
-10 + -1x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2
-10 + -1x + -1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-10 + -1x + -1x2 = 0 + 2x2 + -2x2
-10 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + x + x2)' equal to zero and attempt to solve:

Simplifying
10 + x + x2 = 0

Solving
10 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x + x2 = 0 + -10
x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
x + x2 = -10

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -10 + 0.25

Reorder the terms:
0.25 + x + x2 = -10 + 0.25

Combine like terms: -10 + 0.25 = -9.75
0.25 + x + x2 = -9.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -9.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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