(4x-3)(2x+5)=x+96

Solution for (4x-3)(2x+5)=x+96 equation:

Simplifying
(4x + -3)(2x + 5) = x + 96

Reorder the terms:
(-3 + 4x)(2x + 5) = x + 96

Reorder the terms:
(-3 + 4x)(5 + 2x) = x + 96

Multiply (-3 + 4x) * (5 + 2x)
(-3(5 + 2x) + 4x * (5 + 2x)) = x + 96
((5 * -3 + 2x * -3) + 4x * (5 + 2x)) = x + 96
((-15 + -6x) + 4x * (5 + 2x)) = x + 96
(-15 + -6x + (5 * 4x + 2x * 4x)) = x + 96
(-15 + -6x + (20x + 8x2)) = x + 96

Combine like terms: -6x + 20x = 14x
(-15 + 14x + 8x2) = x + 96

Reorder the terms:
-15 + 14x + 8x2 = 96 + x

Solving
-15 + 14x + 8x2 = 96 + x

Solving for variable 'x'.

Reorder the terms:
-15 + -96 + 14x + -1x + 8x2 = 96 + x + -96 + -1x

Combine like terms: -15 + -96 = -111
-111 + 14x + -1x + 8x2 = 96 + x + -96 + -1x

Combine like terms: 14x + -1x = 13x
-111 + 13x + 8x2 = 96 + x + -96 + -1x

Reorder the terms:
-111 + 13x + 8x2 = 96 + -96 + x + -1x

Combine like terms: 96 + -96 = 0
-111 + 13x + 8x2 = 0 + x + -1x
-111 + 13x + 8x2 = x + -1x

Combine like terms: x + -1x = 0
-111 + 13x + 8x2 = 0

Factor a trinomial.
(-37 + -8x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-37 + -8x)' equal to zero and attempt to solve:

Simplifying
-37 + -8x = 0

Solving
-37 + -8x = 0

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

Add '37' to each side of the equation.
-37 + 37 + -8x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -8x = 0 + 37
-8x = 0 + 37

Combine like terms: 0 + 37 = 37
-8x = 37

Divide each side by '-8'.
x = -4.625

Simplifying
x = -4.625
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4.625, 3}