(x-5)(3x+1)-(x-5)(5x+2)=0

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Solution for (x-5)(3x+1)-(x-5)(5x+2)=0 equation:


Simplifying
(x + -5)(3x + 1) + -1(x + -5)(5x + 2) = 0

Reorder the terms:
(-5 + x)(3x + 1) + -1(x + -5)(5x + 2) = 0

Reorder the terms:
(-5 + x)(1 + 3x) + -1(x + -5)(5x + 2) = 0

Multiply (-5 + x) * (1 + 3x)
(-5(1 + 3x) + x(1 + 3x)) + -1(x + -5)(5x + 2) = 0
((1 * -5 + 3x * -5) + x(1 + 3x)) + -1(x + -5)(5x + 2) = 0
((-5 + -15x) + x(1 + 3x)) + -1(x + -5)(5x + 2) = 0
(-5 + -15x + (1 * x + 3x * x)) + -1(x + -5)(5x + 2) = 0
(-5 + -15x + (1x + 3x2)) + -1(x + -5)(5x + 2) = 0

Combine like terms: -15x + 1x = -14x
(-5 + -14x + 3x2) + -1(x + -5)(5x + 2) = 0

Reorder the terms:
-5 + -14x + 3x2 + -1(-5 + x)(5x + 2) = 0

Reorder the terms:
-5 + -14x + 3x2 + -1(-5 + x)(2 + 5x) = 0

Multiply (-5 + x) * (2 + 5x)
-5 + -14x + 3x2 + -1(-5(2 + 5x) + x(2 + 5x)) = 0
-5 + -14x + 3x2 + -1((2 * -5 + 5x * -5) + x(2 + 5x)) = 0
-5 + -14x + 3x2 + -1((-10 + -25x) + x(2 + 5x)) = 0
-5 + -14x + 3x2 + -1(-10 + -25x + (2 * x + 5x * x)) = 0
-5 + -14x + 3x2 + -1(-10 + -25x + (2x + 5x2)) = 0

Combine like terms: -25x + 2x = -23x
-5 + -14x + 3x2 + -1(-10 + -23x + 5x2) = 0
-5 + -14x + 3x2 + (-10 * -1 + -23x * -1 + 5x2 * -1) = 0
-5 + -14x + 3x2 + (10 + 23x + -5x2) = 0

Reorder the terms:
-5 + 10 + -14x + 23x + 3x2 + -5x2 = 0

Combine like terms: -5 + 10 = 5
5 + -14x + 23x + 3x2 + -5x2 = 0

Combine like terms: -14x + 23x = 9x
5 + 9x + 3x2 + -5x2 = 0

Combine like terms: 3x2 + -5x2 = -2x2
5 + 9x + -2x2 = 0

Solving
5 + 9x + -2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 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 = {5, -0.5}

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