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

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


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

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

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

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

Combine like terms: 10x + -1x = 9x
(-5 + 9x + 2x2) = 3(x + 5)

Reorder the terms:
-5 + 9x + 2x2 = 3(5 + x)
-5 + 9x + 2x2 = (5 * 3 + x * 3)
-5 + 9x + 2x2 = (15 + 3x)

Solving
-5 + 9x + 2x2 = 15 + 3x

Solving for variable 'x'.

Reorder the terms:
-5 + -15 + 9x + -3x + 2x2 = 15 + 3x + -15 + -3x

Combine like terms: -5 + -15 = -20
-20 + 9x + -3x + 2x2 = 15 + 3x + -15 + -3x

Combine like terms: 9x + -3x = 6x
-20 + 6x + 2x2 = 15 + 3x + -15 + -3x

Reorder the terms:
-20 + 6x + 2x2 = 15 + -15 + 3x + -3x

Combine like terms: 15 + -15 = 0
-20 + 6x + 2x2 = 0 + 3x + -3x
-20 + 6x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-20 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 3x + x2) = 0

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

Ignore the factor 2.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}

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