(2x+3)(x-5)=4x+6

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Solution for (2x+3)(x-5)=4x+6 equation: 


Simplifying
(2x + 3)(x + -5) = 4x + 6

Reorder the terms:
(3 + 2x)(x + -5) = 4x + 6

Reorder the terms:
(3 + 2x)(-5 + x) = 4x + 6

Multiply (3 + 2x) * (-5 + x)
(3(-5 + x) + 2x * (-5 + x)) = 4x + 6
((-5 * 3 + x * 3) + 2x * (-5 + x)) = 4x + 6
((-15 + 3x) + 2x * (-5 + x)) = 4x + 6
(-15 + 3x + (-5 * 2x + x * 2x)) = 4x + 6
(-15 + 3x + (-10x + 2x2)) = 4x + 6

Combine like terms: 3x + -10x = -7x
(-15 + -7x + 2x2) = 4x + 6

Reorder the terms:
-15 + -7x + 2x2 = 6 + 4x

Solving
-15 + -7x + 2x2 = 6 + 4x

Solving for variable 'x'.

Reorder the terms:
-15 + -6 + -7x + -4x + 2x2 = 6 + 4x + -6 + -4x

Combine like terms: -15 + -6 = -21
-21 + -7x + -4x + 2x2 = 6 + 4x + -6 + -4x

Combine like terms: -7x + -4x = -11x
-21 + -11x + 2x2 = 6 + 4x + -6 + -4x

Reorder the terms:
-21 + -11x + 2x2 = 6 + -6 + 4x + -4x

Combine like terms: 6 + -6 = 0
-21 + -11x + 2x2 = 0 + 4x + -4x
-21 + -11x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-21 + -11x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.5, 7}

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