=(2x-3)(4x-7)

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Solution for =(2x-3)(4x-7) equation: 


Simplifying
0 = (2x + -3)(4x + -7)

Reorder the terms:
0 = (-3 + 2x)(4x + -7)

Reorder the terms:
0 = (-3 + 2x)(-7 + 4x)

Multiply (-3 + 2x) * (-7 + 4x)
0 = (-3(-7 + 4x) + 2x * (-7 + 4x))
0 = ((-7 * -3 + 4x * -3) + 2x * (-7 + 4x))
0 = ((21 + -12x) + 2x * (-7 + 4x))
0 = (21 + -12x + (-7 * 2x + 4x * 2x))
0 = (21 + -12x + (-14x + 8x2))

Combine like terms: -12x + -14x = -26x
0 = (21 + -26x + 8x2)

Solving
0 = 21 + -26x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -21 = -21
-21 + 26x + -8x2 = 21 + -26x + 8x2 + -21 + 26x + -8x2

Reorder the terms:
-21 + 26x + -8x2 = 21 + -21 + -26x + 26x + 8x2 + -8x2

Combine like terms: 21 + -21 = 0
-21 + 26x + -8x2 = 0 + -26x + 26x + 8x2 + -8x2
-21 + 26x + -8x2 = -26x + 26x + 8x2 + -8x2

Combine like terms: -26x + 26x = 0
-21 + 26x + -8x2 = 0 + 8x2 + -8x2
-21 + 26x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-21 + 26x + -8x2 = 0

Factor a trinomial.
(-7 + 4x)(3 + -2x) = 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {1.75, 1.5}

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