(2x+3)(x-4)=10x+15

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Solution for (2x+3)(x-4)=10x+15 equation: 


Simplifying
(2x + 3)(x + -4) = 10x + 15

Reorder the terms:
(3 + 2x)(x + -4) = 10x + 15

Reorder the terms:
(3 + 2x)(-4 + x) = 10x + 15

Multiply (3 + 2x) * (-4 + x)
(3(-4 + x) + 2x * (-4 + x)) = 10x + 15
((-4 * 3 + x * 3) + 2x * (-4 + x)) = 10x + 15
((-12 + 3x) + 2x * (-4 + x)) = 10x + 15
(-12 + 3x + (-4 * 2x + x * 2x)) = 10x + 15
(-12 + 3x + (-8x + 2x2)) = 10x + 15

Combine like terms: 3x + -8x = -5x
(-12 + -5x + 2x2) = 10x + 15

Reorder the terms:
-12 + -5x + 2x2 = 15 + 10x

Solving
-12 + -5x + 2x2 = 15 + 10x

Solving for variable 'x'.

Reorder the terms:
-12 + -15 + -5x + -10x + 2x2 = 15 + 10x + -15 + -10x

Combine like terms: -12 + -15 = -27
-27 + -5x + -10x + 2x2 = 15 + 10x + -15 + -10x

Combine like terms: -5x + -10x = -15x
-27 + -15x + 2x2 = 15 + 10x + -15 + -10x

Reorder the terms:
-27 + -15x + 2x2 = 15 + -15 + 10x + -10x

Combine like terms: 15 + -15 = 0
-27 + -15x + 2x2 = 0 + 10x + -10x
-27 + -15x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-27 + -15x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1.5, 9}

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