4x(x-1)+5=2x+9

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Solution for 4x(x-1)+5=2x+9 equation: 


Simplifying
4x(x + -1) + 5 = 2x + 9

Reorder the terms:
4x(-1 + x) + 5 = 2x + 9
(-1 * 4x + x * 4x) + 5 = 2x + 9
(-4x + 4x2) + 5 = 2x + 9

Reorder the terms:
5 + -4x + 4x2 = 2x + 9

Reorder the terms:
5 + -4x + 4x2 = 9 + 2x

Solving
5 + -4x + 4x2 = 9 + 2x

Solving for variable 'x'.

Reorder the terms:
5 + -9 + -4x + -2x + 4x2 = 9 + 2x + -9 + -2x

Combine like terms: 5 + -9 = -4
-4 + -4x + -2x + 4x2 = 9 + 2x + -9 + -2x

Combine like terms: -4x + -2x = -6x
-4 + -6x + 4x2 = 9 + 2x + -9 + -2x

Reorder the terms:
-4 + -6x + 4x2 = 9 + -9 + 2x + -2x

Combine like terms: 9 + -9 = 0
-4 + -6x + 4x2 = 0 + 2x + -2x
-4 + -6x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + -6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -3x + 2x2) = 0

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

Ignore the factor 2.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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 = {-0.5, 2}

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