(4x-5)(2x-3)=105

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Solution for (4x-5)(2x-3)=105 equation: 


Simplifying
(4x + -5)(2x + -3) = 105

Reorder the terms:
(-5 + 4x)(2x + -3) = 105

Reorder the terms:
(-5 + 4x)(-3 + 2x) = 105

Multiply (-5 + 4x) * (-3 + 2x)
(-5(-3 + 2x) + 4x * (-3 + 2x)) = 105
((-3 * -5 + 2x * -5) + 4x * (-3 + 2x)) = 105
((15 + -10x) + 4x * (-3 + 2x)) = 105
(15 + -10x + (-3 * 4x + 2x * 4x)) = 105
(15 + -10x + (-12x + 8x2)) = 105

Combine like terms: -10x + -12x = -22x
(15 + -22x + 8x2) = 105

Solving
15 + -22x + 8x2 = 105

Solving for variable 'x'.

Reorder the terms:
15 + -105 + -22x + 8x2 = 105 + -105

Combine like terms: 15 + -105 = -90
-90 + -22x + 8x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-90 + -22x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -11x + 4x2) = 0

Factor a trinomial.
2((-9 + -4x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 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 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2.25, 5}

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