(2x+5)(x-5)=6x+15

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Solution for (2x+5)(x-5)=6x+15 equation: 


Simplifying
(2x + 5)(x + -5) = 6x + 15

Reorder the terms:
(5 + 2x)(x + -5) = 6x + 15

Reorder the terms:
(5 + 2x)(-5 + x) = 6x + 15

Multiply (5 + 2x) * (-5 + x)
(5(-5 + x) + 2x * (-5 + x)) = 6x + 15
((-5 * 5 + x * 5) + 2x * (-5 + x)) = 6x + 15
((-25 + 5x) + 2x * (-5 + x)) = 6x + 15
(-25 + 5x + (-5 * 2x + x * 2x)) = 6x + 15
(-25 + 5x + (-10x + 2x2)) = 6x + 15

Combine like terms: 5x + -10x = -5x
(-25 + -5x + 2x2) = 6x + 15

Reorder the terms:
-25 + -5x + 2x2 = 15 + 6x

Solving
-25 + -5x + 2x2 = 15 + 6x

Solving for variable 'x'.

Reorder the terms:
-25 + -15 + -5x + -6x + 2x2 = 15 + 6x + -15 + -6x

Combine like terms: -25 + -15 = -40
-40 + -5x + -6x + 2x2 = 15 + 6x + -15 + -6x

Combine like terms: -5x + -6x = -11x
-40 + -11x + 2x2 = 15 + 6x + -15 + -6x

Reorder the terms:
-40 + -11x + 2x2 = 15 + -15 + 6x + -6x

Combine like terms: 15 + -15 = 0
-40 + -11x + 2x2 = 0 + 6x + -6x
-40 + -11x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-40 + -11x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-2.5, 8}

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