(4a-1)(a-2)-7a+5=0

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Solution for (4a-1)(a-2)-7a+5=0 equation: 


Simplifying
(4a + -1)(a + -2) + -7a + 5 = 0

Reorder the terms:
(-1 + 4a)(a + -2) + -7a + 5 = 0

Reorder the terms:
(-1 + 4a)(-2 + a) + -7a + 5 = 0

Multiply (-1 + 4a) * (-2 + a)
(-1(-2 + a) + 4a * (-2 + a)) + -7a + 5 = 0
((-2 * -1 + a * -1) + 4a * (-2 + a)) + -7a + 5 = 0
((2 + -1a) + 4a * (-2 + a)) + -7a + 5 = 0
(2 + -1a + (-2 * 4a + a * 4a)) + -7a + 5 = 0
(2 + -1a + (-8a + 4a2)) + -7a + 5 = 0

Combine like terms: -1a + -8a = -9a
(2 + -9a + 4a2) + -7a + 5 = 0

Reorder the terms:
2 + 5 + -9a + -7a + 4a2 = 0

Combine like terms: 2 + 5 = 7
7 + -9a + -7a + 4a2 = 0

Combine like terms: -9a + -7a = -16a
7 + -16a + 4a2 = 0

Solving
7 + -16a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -2a)(7 + -2a) = 0


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

Simplifying
1 + -2a = 0

Solving
1 + -2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2a = 0 + -1

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

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

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

Simplifying
a = 0.5

Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve:

Simplifying
7 + -2a = 0

Solving
7 + -2a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {0.5, 3.5}

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