(5x-4)(3x-2)-(3x-2)(-8x-7)=0

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Solution for (5x-4)(3x-2)-(3x-2)(-8x-7)=0 equation:


Simplifying
(5x + -4)(3x + -2) + -1(3x + -2)(-8x + -7) = 0

Reorder the terms:
(-4 + 5x)(3x + -2) + -1(3x + -2)(-8x + -7) = 0

Reorder the terms:
(-4 + 5x)(-2 + 3x) + -1(3x + -2)(-8x + -7) = 0

Multiply (-4 + 5x) * (-2 + 3x)
(-4(-2 + 3x) + 5x * (-2 + 3x)) + -1(3x + -2)(-8x + -7) = 0
((-2 * -4 + 3x * -4) + 5x * (-2 + 3x)) + -1(3x + -2)(-8x + -7) = 0
((8 + -12x) + 5x * (-2 + 3x)) + -1(3x + -2)(-8x + -7) = 0
(8 + -12x + (-2 * 5x + 3x * 5x)) + -1(3x + -2)(-8x + -7) = 0
(8 + -12x + (-10x + 15x2)) + -1(3x + -2)(-8x + -7) = 0

Combine like terms: -12x + -10x = -22x
(8 + -22x + 15x2) + -1(3x + -2)(-8x + -7) = 0

Reorder the terms:
8 + -22x + 15x2 + -1(-2 + 3x)(-8x + -7) = 0

Reorder the terms:
8 + -22x + 15x2 + -1(-2 + 3x)(-7 + -8x) = 0

Multiply (-2 + 3x) * (-7 + -8x)
8 + -22x + 15x2 + -1(-2(-7 + -8x) + 3x * (-7 + -8x)) = 0
8 + -22x + 15x2 + -1((-7 * -2 + -8x * -2) + 3x * (-7 + -8x)) = 0
8 + -22x + 15x2 + -1((14 + 16x) + 3x * (-7 + -8x)) = 0
8 + -22x + 15x2 + -1(14 + 16x + (-7 * 3x + -8x * 3x)) = 0
8 + -22x + 15x2 + -1(14 + 16x + (-21x + -24x2)) = 0

Combine like terms: 16x + -21x = -5x
8 + -22x + 15x2 + -1(14 + -5x + -24x2) = 0
8 + -22x + 15x2 + (14 * -1 + -5x * -1 + -24x2 * -1) = 0
8 + -22x + 15x2 + (-14 + 5x + 24x2) = 0

Reorder the terms:
8 + -14 + -22x + 5x + 15x2 + 24x2 = 0

Combine like terms: 8 + -14 = -6
-6 + -22x + 5x + 15x2 + 24x2 = 0

Combine like terms: -22x + 5x = -17x
-6 + -17x + 15x2 + 24x2 = 0

Combine like terms: 15x2 + 24x2 = 39x2
-6 + -17x + 39x2 = 0

Solving
-6 + -17x + 39x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -13x)(2 + -3x) = 0

Subproblem 1

Set the factor '(-3 + -13x)' equal to zero and attempt to solve: Simplifying -3 + -13x = 0 Solving -3 + -13x = 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 + -13x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -13x = 0 + 3 -13x = 0 + 3 Combine like terms: 0 + 3 = 3 -13x = 3 Divide each side by '-13'. x = -0.2307692308 Simplifying x = -0.2307692308

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {-0.2307692308, 0.6666666667}

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