(x-5)(x+1)+(x-5)(2x-3)=10

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Solution for (x-5)(x+1)+(x-5)(2x-3)=10 equation: 


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

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

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

Multiply (-5 + x) * (1 + x)
(-5(1 + x) + x(1 + x)) + (x + -5)(2x + -3) = 10
((1 * -5 + x * -5) + x(1 + x)) + (x + -5)(2x + -3) = 10
((-5 + -5x) + x(1 + x)) + (x + -5)(2x + -3) = 10
(-5 + -5x + (1 * x + x * x)) + (x + -5)(2x + -3) = 10
(-5 + -5x + (1x + x2)) + (x + -5)(2x + -3) = 10

Combine like terms: -5x + 1x = -4x
(-5 + -4x + x2) + (x + -5)(2x + -3) = 10

Reorder the terms:
-5 + -4x + x2 + (-5 + x)(2x + -3) = 10

Reorder the terms:
-5 + -4x + x2 + (-5 + x)(-3 + 2x) = 10

Multiply (-5 + x) * (-3 + 2x)
-5 + -4x + x2 + (-5(-3 + 2x) + x(-3 + 2x)) = 10
-5 + -4x + x2 + ((-3 * -5 + 2x * -5) + x(-3 + 2x)) = 10
-5 + -4x + x2 + ((15 + -10x) + x(-3 + 2x)) = 10
-5 + -4x + x2 + (15 + -10x + (-3 * x + 2x * x)) = 10
-5 + -4x + x2 + (15 + -10x + (-3x + 2x2)) = 10

Combine like terms: -10x + -3x = -13x
-5 + -4x + x2 + (15 + -13x + 2x2) = 10

Reorder the terms:
-5 + 15 + -4x + -13x + x2 + 2x2 = 10

Combine like terms: -5 + 15 = 10
10 + -4x + -13x + x2 + 2x2 = 10

Combine like terms: -4x + -13x = -17x
10 + -17x + x2 + 2x2 = 10

Combine like terms: x2 + 2x2 = 3x2
10 + -17x + 3x2 = 10

Add '-10' to each side of the equation.
10 + -17x + -10 + 3x2 = 10 + -10

Reorder the terms:
10 + -10 + -17x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
0 + -17x + 3x2 = 10 + -10
-17x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-17x + 3x2 = 0

Solving
-17x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-17 + 3x) = 0


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 '(-17 + 3x)' equal to zero and attempt to solve:

Simplifying
-17 + 3x = 0

Solving
-17 + 3x = 0

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

Add '17' to each side of the equation.
-17 + 17 + 3x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 3x = 0 + 17
3x = 0 + 17

Combine like terms: 0 + 17 = 17
3x = 17

Divide each side by '3'.
x = 5.666666667

Simplifying
x = 5.666666667
Solution
x = {0, 5.666666667}

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