(2X-1)(X-4)=147

Solution for (2X-1)(X-4)=147 equation:

Simplifying
(2X + -1)(X + -4) = 147

Reorder the terms:
(-1 + 2X)(X + -4) = 147

Reorder the terms:
(-1 + 2X)(-4 + X) = 147

Multiply (-1 + 2X) * (-4 + X)
(-1(-4 + X) + 2X * (-4 + X)) = 147
((-4 * -1 + X * -1) + 2X * (-4 + X)) = 147
((4 + -1X) + 2X * (-4 + X)) = 147
(4 + -1X + (-4 * 2X + X * 2X)) = 147
(4 + -1X + (-8X + 2X2)) = 147

Combine like terms: -1X + -8X = -9X
(4 + -9X + 2X2) = 147

Solving
4 + -9X + 2X2 = 147

Solving for variable 'X'.

Reorder the terms:
4 + -147 + -9X + 2X2 = 147 + -147

Combine like terms: 4 + -147 = -143
-143 + -9X + 2X2 = 147 + -147

Combine like terms: 147 + -147 = 0
-143 + -9X + 2X2 = 0

Factor a trinomial.
(-13 + -2X)(11 + -1X) = 0

Subproblem 1
Set the factor '(-13 + -2X)' equal to zero and attempt to solve:

Simplifying
-13 + -2X = 0

Solving
-13 + -2X = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2X = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2X = 0 + 13
-2X = 0 + 13

Combine like terms: 0 + 13 = 13
-2X = 13

Divide each side by '-2'.
X = -6.5

Simplifying
X = -6.5
Subproblem 2
Set the factor '(11 + -1X)' equal to zero and attempt to solve:

Simplifying
11 + -1X = 0

Solving
11 + -1X = 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 + -1X = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1X = 0 + -11
-1X = 0 + -11

Combine like terms: 0 + -11 = -11
-1X = -11

Divide each side by '-1'.
X = 11

Simplifying
X = 11
Solution
X = {-6.5, 11}