x(2x+3)=-4x(x-1)+15

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Solution for x(2x+3)=-4x(x-1)+15 equation: 


Simplifying
x(2x + 3) = -4x(x + -1) + 15

Reorder the terms:
x(3 + 2x) = -4x(x + -1) + 15
(3 * x + 2x * x) = -4x(x + -1) + 15
(3x + 2x2) = -4x(x + -1) + 15

Reorder the terms:
3x + 2x2 = -4x(-1 + x) + 15
3x + 2x2 = (-1 * -4x + x * -4x) + 15
3x + 2x2 = (4x + -4x2) + 15

Reorder the terms:
3x + 2x2 = 15 + 4x + -4x2

Solving
3x + 2x2 = 15 + 4x + -4x2

Solving for variable 'x'.

Reorder the terms:
-15 + 3x + -4x + 2x2 + 4x2 = 15 + 4x + -4x2 + -15 + -4x + 4x2

Combine like terms: 3x + -4x = -1x
-15 + -1x + 2x2 + 4x2 = 15 + 4x + -4x2 + -15 + -4x + 4x2

Combine like terms: 2x2 + 4x2 = 6x2
-15 + -1x + 6x2 = 15 + 4x + -4x2 + -15 + -4x + 4x2

Reorder the terms:
-15 + -1x + 6x2 = 15 + -15 + 4x + -4x + -4x2 + 4x2

Combine like terms: 15 + -15 = 0
-15 + -1x + 6x2 = 0 + 4x + -4x + -4x2 + 4x2
-15 + -1x + 6x2 = 4x + -4x + -4x2 + 4x2

Combine like terms: 4x + -4x = 0
-15 + -1x + 6x2 = 0 + -4x2 + 4x2
-15 + -1x + 6x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-15 + -1x + 6x2 = 0

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


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, 1.666666667}

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