(4x+5)(2x-1)=4

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Solution for (4x+5)(2x-1)=4 equation: 


Simplifying
(4x + 5)(2x + -1) = 4

Reorder the terms:
(5 + 4x)(2x + -1) = 4

Reorder the terms:
(5 + 4x)(-1 + 2x) = 4

Multiply (5 + 4x) * (-1 + 2x)
(5(-1 + 2x) + 4x * (-1 + 2x)) = 4
((-1 * 5 + 2x * 5) + 4x * (-1 + 2x)) = 4
((-5 + 10x) + 4x * (-1 + 2x)) = 4
(-5 + 10x + (-1 * 4x + 2x * 4x)) = 4
(-5 + 10x + (-4x + 8x2)) = 4

Combine like terms: 10x + -4x = 6x
(-5 + 6x + 8x2) = 4

Solving
-5 + 6x + 8x2 = 4

Solving for variable 'x'.

Reorder the terms:
-5 + -4 + 6x + 8x2 = 4 + -4

Combine like terms: -5 + -4 = -9
-9 + 6x + 8x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-9 + 6x + 8x2 = 0

Factor a trinomial.
(-3 + -2x)(3 + -4x) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1.5, 0.75}

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