(4x-5)(x+2)=12

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Solution for (4x-5)(x+2)=12 equation: 


Simplifying
(4x + -5)(x + 2) = 12

Reorder the terms:
(-5 + 4x)(x + 2) = 12

Reorder the terms:
(-5 + 4x)(2 + x) = 12

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

Combine like terms: -5x + 8x = 3x
(-10 + 3x + 4x2) = 12

Solving
-10 + 3x + 4x2 = 12

Solving for variable 'x'.

Reorder the terms:
-10 + -12 + 3x + 4x2 = 12 + -12

Combine like terms: -10 + -12 = -22
-22 + 3x + 4x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-22 + 3x + 4x2 = 0

Factor a trinomial.
(-11 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -4x)' equal to zero and attempt to solve:

Simplifying
-11 + -4x = 0

Solving
-11 + -4x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -4x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4x = 0 + 11
-4x = 0 + 11

Combine like terms: 0 + 11 = 11
-4x = 11

Divide each side by '-4'.
x = -2.75

Simplifying
x = -2.75

Subproblem 2
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
Solution
x = {-2.75, 2}

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