(8x+3)(2x-5)-(3x+5)(3x-5)=22x+10

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Solution for (8x+3)(2x-5)-(3x+5)(3x-5)=22x+10 equation: 


Simplifying
(8x + 3)(2x + -5) + -1(3x + 5)(3x + -5) = 22x + 10

Reorder the terms:
(3 + 8x)(2x + -5) + -1(3x + 5)(3x + -5) = 22x + 10

Reorder the terms:
(3 + 8x)(-5 + 2x) + -1(3x + 5)(3x + -5) = 22x + 10

Multiply (3 + 8x) * (-5 + 2x)
(3(-5 + 2x) + 8x * (-5 + 2x)) + -1(3x + 5)(3x + -5) = 22x + 10
((-5 * 3 + 2x * 3) + 8x * (-5 + 2x)) + -1(3x + 5)(3x + -5) = 22x + 10
((-15 + 6x) + 8x * (-5 + 2x)) + -1(3x + 5)(3x + -5) = 22x + 10
(-15 + 6x + (-5 * 8x + 2x * 8x)) + -1(3x + 5)(3x + -5) = 22x + 10
(-15 + 6x + (-40x + 16x2)) + -1(3x + 5)(3x + -5) = 22x + 10

Combine like terms: 6x + -40x = -34x
(-15 + -34x + 16x2) + -1(3x + 5)(3x + -5) = 22x + 10

Reorder the terms:
-15 + -34x + 16x2 + -1(5 + 3x)(3x + -5) = 22x + 10

Reorder the terms:
-15 + -34x + 16x2 + -1(5 + 3x)(-5 + 3x) = 22x + 10

Multiply (5 + 3x) * (-5 + 3x)
-15 + -34x + 16x2 + -1(5(-5 + 3x) + 3x * (-5 + 3x)) = 22x + 10
-15 + -34x + 16x2 + -1((-5 * 5 + 3x * 5) + 3x * (-5 + 3x)) = 22x + 10
-15 + -34x + 16x2 + -1((-25 + 15x) + 3x * (-5 + 3x)) = 22x + 10
-15 + -34x + 16x2 + -1(-25 + 15x + (-5 * 3x + 3x * 3x)) = 22x + 10
-15 + -34x + 16x2 + -1(-25 + 15x + (-15x + 9x2)) = 22x + 10

Combine like terms: 15x + -15x = 0
-15 + -34x + 16x2 + -1(-25 + 0 + 9x2) = 22x + 10
-15 + -34x + 16x2 + -1(-25 + 9x2) = 22x + 10
-15 + -34x + 16x2 + (-25 * -1 + 9x2 * -1) = 22x + 10
-15 + -34x + 16x2 + (25 + -9x2) = 22x + 10

Reorder the terms:
-15 + 25 + -34x + 16x2 + -9x2 = 22x + 10

Combine like terms: -15 + 25 = 10
10 + -34x + 16x2 + -9x2 = 22x + 10

Combine like terms: 16x2 + -9x2 = 7x2
10 + -34x + 7x2 = 22x + 10

Reorder the terms:
10 + -34x + 7x2 = 10 + 22x

Add '-10' to each side of the equation.
10 + -34x + -10 + 7x2 = 10 + -10 + 22x

Reorder the terms:
10 + -10 + -34x + 7x2 = 10 + -10 + 22x

Combine like terms: 10 + -10 = 0
0 + -34x + 7x2 = 10 + -10 + 22x
-34x + 7x2 = 10 + -10 + 22x

Combine like terms: 10 + -10 = 0
-34x + 7x2 = 0 + 22x
-34x + 7x2 = 22x

Solving
-34x + 7x2 = 22x

Solving for variable 'x'.

Reorder the terms:
-34x + -22x + 7x2 = 22x + -22x

Combine like terms: -34x + -22x = -56x
-56x + 7x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
-56x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(-8 + x) = 0

Ignore the factor 7.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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