(4x-7)(2-3x)+(4x-7)(4x+5)=0

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Solution for (4x-7)(2-3x)+(4x-7)(4x+5)=0 equation:


Simplifying
(4x + -7)(2 + -3x) + (4x + -7)(4x + 5) = 0

Reorder the terms:
(-7 + 4x)(2 + -3x) + (4x + -7)(4x + 5) = 0

Multiply (-7 + 4x) * (2 + -3x)
(-7(2 + -3x) + 4x * (2 + -3x)) + (4x + -7)(4x + 5) = 0
((2 * -7 + -3x * -7) + 4x * (2 + -3x)) + (4x + -7)(4x + 5) = 0
((-14 + 21x) + 4x * (2 + -3x)) + (4x + -7)(4x + 5) = 0
(-14 + 21x + (2 * 4x + -3x * 4x)) + (4x + -7)(4x + 5) = 0
(-14 + 21x + (8x + -12x2)) + (4x + -7)(4x + 5) = 0

Combine like terms: 21x + 8x = 29x
(-14 + 29x + -12x2) + (4x + -7)(4x + 5) = 0

Reorder the terms:
-14 + 29x + -12x2 + (-7 + 4x)(4x + 5) = 0

Reorder the terms:
-14 + 29x + -12x2 + (-7 + 4x)(5 + 4x) = 0

Multiply (-7 + 4x) * (5 + 4x)
-14 + 29x + -12x2 + (-7(5 + 4x) + 4x * (5 + 4x)) = 0
-14 + 29x + -12x2 + ((5 * -7 + 4x * -7) + 4x * (5 + 4x)) = 0
-14 + 29x + -12x2 + ((-35 + -28x) + 4x * (5 + 4x)) = 0
-14 + 29x + -12x2 + (-35 + -28x + (5 * 4x + 4x * 4x)) = 0
-14 + 29x + -12x2 + (-35 + -28x + (20x + 16x2)) = 0

Combine like terms: -28x + 20x = -8x
-14 + 29x + -12x2 + (-35 + -8x + 16x2) = 0

Reorder the terms:
-14 + -35 + 29x + -8x + -12x2 + 16x2 = 0

Combine like terms: -14 + -35 = -49
-49 + 29x + -8x + -12x2 + 16x2 = 0

Combine like terms: 29x + -8x = 21x
-49 + 21x + -12x2 + 16x2 = 0

Combine like terms: -12x2 + 16x2 = 4x2
-49 + 21x + 4x2 = 0

Solving
-49 + 21x + 4x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

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

Solution

x = {-7, 1.75}

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