(2x+15)(3x-4)=(2x+15)

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Solution for (2x+15)(3x-4)=(2x+15) equation: 


Simplifying
(2x + 15)(3x + -4) = (2x + 15)

Reorder the terms:
(15 + 2x)(3x + -4) = (2x + 15)

Reorder the terms:
(15 + 2x)(-4 + 3x) = (2x + 15)

Multiply (15 + 2x) * (-4 + 3x)
(15(-4 + 3x) + 2x * (-4 + 3x)) = (2x + 15)
((-4 * 15 + 3x * 15) + 2x * (-4 + 3x)) = (2x + 15)
((-60 + 45x) + 2x * (-4 + 3x)) = (2x + 15)
(-60 + 45x + (-4 * 2x + 3x * 2x)) = (2x + 15)
(-60 + 45x + (-8x + 6x2)) = (2x + 15)

Combine like terms: 45x + -8x = 37x
(-60 + 37x + 6x2) = (2x + 15)

Reorder the terms:
-60 + 37x + 6x2 = (15 + 2x)

Remove parenthesis around (15 + 2x)
-60 + 37x + 6x2 = 15 + 2x

Solving
-60 + 37x + 6x2 = 15 + 2x

Solving for variable 'x'.

Reorder the terms:
-60 + -15 + 37x + -2x + 6x2 = 15 + 2x + -15 + -2x

Combine like terms: -60 + -15 = -75
-75 + 37x + -2x + 6x2 = 15 + 2x + -15 + -2x

Combine like terms: 37x + -2x = 35x
-75 + 35x + 6x2 = 15 + 2x + -15 + -2x

Reorder the terms:
-75 + 35x + 6x2 = 15 + -15 + 2x + -2x

Combine like terms: 15 + -15 = 0
-75 + 35x + 6x2 = 0 + 2x + -2x
-75 + 35x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-75 + 35x + 6x2 = 0

Factor a trinomial.
(-15 + -2x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-7.5, 1.666666667}

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