(4x-7)(x-2)=0

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Solution for (4x-7)(x-2)=0 equation: 


Simplifying
(4x + -7)(x + -2) = 0

Reorder the terms:
(-7 + 4x)(x + -2) = 0

Reorder the terms:
(-7 + 4x)(-2 + x) = 0

Multiply (-7 + 4x) * (-2 + x)
(-7(-2 + x) + 4x * (-2 + x)) = 0
((-2 * -7 + x * -7) + 4x * (-2 + x)) = 0
((14 + -7x) + 4x * (-2 + x)) = 0
(14 + -7x + (-2 * 4x + x * 4x)) = 0
(14 + -7x + (-8x + 4x2)) = 0

Combine like terms: -7x + -8x = -15x
(14 + -15x + 4x2) = 0

Solving
14 + -15x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

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

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

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75

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 = {1.75, 2}

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