(4x+5)(3x-2)=24

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Solution for (4x+5)(3x-2)=24 equation: 


Simplifying
(4x + 5)(3x + -2) = 24

Reorder the terms:
(5 + 4x)(3x + -2) = 24

Reorder the terms:
(5 + 4x)(-2 + 3x) = 24

Multiply (5 + 4x) * (-2 + 3x)
(5(-2 + 3x) + 4x * (-2 + 3x)) = 24
((-2 * 5 + 3x * 5) + 4x * (-2 + 3x)) = 24
((-10 + 15x) + 4x * (-2 + 3x)) = 24
(-10 + 15x + (-2 * 4x + 3x * 4x)) = 24
(-10 + 15x + (-8x + 12x2)) = 24

Combine like terms: 15x + -8x = 7x
(-10 + 7x + 12x2) = 24

Solving
-10 + 7x + 12x2 = 24

Solving for variable 'x'.

Reorder the terms:
-10 + -24 + 7x + 12x2 = 24 + -24

Combine like terms: -10 + -24 = -34
-34 + 7x + 12x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-34 + 7x + 12x2 = 0

Factor a trinomial.
(-2 + -1x)(17 + -12x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(17 + -12x)' equal to zero and attempt to solve:

Simplifying
17 + -12x = 0

Solving
17 + -12x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -12x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -12x = 0 + -17
-12x = 0 + -17

Combine like terms: 0 + -17 = -17
-12x = -17

Divide each side by '-12'.
x = 1.416666667

Simplifying
x = 1.416666667
Solution
x = {-2, 1.416666667}

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