(4x-1)(x-2)=7x-5

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Solution for (4x-1)(x-2)=7x-5 equation: 


Simplifying
(4x + -1)(x + -2) = 7x + -5

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

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

Multiply (-1 + 4x) * (-2 + x)
(-1(-2 + x) + 4x * (-2 + x)) = 7x + -5
((-2 * -1 + x * -1) + 4x * (-2 + x)) = 7x + -5
((2 + -1x) + 4x * (-2 + x)) = 7x + -5
(2 + -1x + (-2 * 4x + x * 4x)) = 7x + -5
(2 + -1x + (-8x + 4x2)) = 7x + -5

Combine like terms: -1x + -8x = -9x
(2 + -9x + 4x2) = 7x + -5

Reorder the terms:
2 + -9x + 4x2 = -5 + 7x

Solving
2 + -9x + 4x2 = -5 + 7x

Solving for variable 'x'.

Reorder the terms:
2 + 5 + -9x + -7x + 4x2 = -5 + 7x + 5 + -7x

Combine like terms: 2 + 5 = 7
7 + -9x + -7x + 4x2 = -5 + 7x + 5 + -7x

Combine like terms: -9x + -7x = -16x
7 + -16x + 4x2 = -5 + 7x + 5 + -7x

Reorder the terms:
7 + -16x + 4x2 = -5 + 5 + 7x + -7x

Combine like terms: -5 + 5 = 0
7 + -16x + 4x2 = 0 + 7x + -7x
7 + -16x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
7 + -16x + 4x2 = 0

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


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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

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

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

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

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

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

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