(4x-1)(x+2)=9

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Solution for (4x-1)(x+2)=9 equation: 


Simplifying
(4x + -1)(x + 2) = 9

Reorder the terms:
(-1 + 4x)(x + 2) = 9

Reorder the terms:
(-1 + 4x)(2 + x) = 9

Multiply (-1 + 4x) * (2 + x)
(-1(2 + x) + 4x * (2 + x)) = 9
((2 * -1 + x * -1) + 4x * (2 + x)) = 9
((-2 + -1x) + 4x * (2 + x)) = 9
(-2 + -1x + (2 * 4x + x * 4x)) = 9
(-2 + -1x + (8x + 4x2)) = 9

Combine like terms: -1x + 8x = 7x
(-2 + 7x + 4x2) = 9

Solving
-2 + 7x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
-2 + -9 + 7x + 4x2 = 9 + -9

Combine like terms: -2 + -9 = -11
-11 + 7x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-11 + 7x + 4x2 = 0

Factor a trinomial.
(-11 + -4x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.75, 1}

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