(4x-7)(2x+3)=3(4x-7)(5x+11)

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Solution for (4x-7)(2x+3)=3(4x-7)(5x+11) equation:


Simplifying
(4x + -7)(2x + 3) = 3(4x + -7)(5x + 11)

Reorder the terms:
(-7 + 4x)(2x + 3) = 3(4x + -7)(5x + 11)

Reorder the terms:
(-7 + 4x)(3 + 2x) = 3(4x + -7)(5x + 11)

Multiply (-7 + 4x) * (3 + 2x)
(-7(3 + 2x) + 4x * (3 + 2x)) = 3(4x + -7)(5x + 11)
((3 * -7 + 2x * -7) + 4x * (3 + 2x)) = 3(4x + -7)(5x + 11)
((-21 + -14x) + 4x * (3 + 2x)) = 3(4x + -7)(5x + 11)
(-21 + -14x + (3 * 4x + 2x * 4x)) = 3(4x + -7)(5x + 11)
(-21 + -14x + (12x + 8x2)) = 3(4x + -7)(5x + 11)

Combine like terms: -14x + 12x = -2x
(-21 + -2x + 8x2) = 3(4x + -7)(5x + 11)

Reorder the terms:
-21 + -2x + 8x2 = 3(-7 + 4x)(5x + 11)

Reorder the terms:
-21 + -2x + 8x2 = 3(-7 + 4x)(11 + 5x)

Multiply (-7 + 4x) * (11 + 5x)
-21 + -2x + 8x2 = 3(-7(11 + 5x) + 4x * (11 + 5x))
-21 + -2x + 8x2 = 3((11 * -7 + 5x * -7) + 4x * (11 + 5x))
-21 + -2x + 8x2 = 3((-77 + -35x) + 4x * (11 + 5x))
-21 + -2x + 8x2 = 3(-77 + -35x + (11 * 4x + 5x * 4x))
-21 + -2x + 8x2 = 3(-77 + -35x + (44x + 20x2))

Combine like terms: -35x + 44x = 9x
-21 + -2x + 8x2 = 3(-77 + 9x + 20x2)
-21 + -2x + 8x2 = (-77 * 3 + 9x * 3 + 20x2 * 3)
-21 + -2x + 8x2 = (-231 + 27x + 60x2)

Solving
-21 + -2x + 8x2 = -231 + 27x + 60x2

Solving for variable 'x'.

Reorder the terms:
-21 + 231 + -2x + -27x + 8x2 + -60x2 = -231 + 27x + 60x2 + 231 + -27x + -60x2

Combine like terms: -21 + 231 = 210
210 + -2x + -27x + 8x2 + -60x2 = -231 + 27x + 60x2 + 231 + -27x + -60x2

Combine like terms: -2x + -27x = -29x
210 + -29x + 8x2 + -60x2 = -231 + 27x + 60x2 + 231 + -27x + -60x2

Combine like terms: 8x2 + -60x2 = -52x2
210 + -29x + -52x2 = -231 + 27x + 60x2 + 231 + -27x + -60x2

Reorder the terms:
210 + -29x + -52x2 = -231 + 231 + 27x + -27x + 60x2 + -60x2

Combine like terms: -231 + 231 = 0
210 + -29x + -52x2 = 0 + 27x + -27x + 60x2 + -60x2
210 + -29x + -52x2 = 27x + -27x + 60x2 + -60x2

Combine like terms: 27x + -27x = 0
210 + -29x + -52x2 = 0 + 60x2 + -60x2
210 + -29x + -52x2 = 60x2 + -60x2

Combine like terms: 60x2 + -60x2 = 0
210 + -29x + -52x2 = 0

Factor a trinomial.
(7 + -4x)(30 + 13x) = 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 '(30 + 13x)' equal to zero and attempt to solve: Simplifying 30 + 13x = 0 Solving 30 + 13x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + 13x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 13x = 0 + -30 13x = 0 + -30 Combine like terms: 0 + -30 = -30 13x = -30 Divide each side by '13'. x = -2.307692308 Simplifying x = -2.307692308

Solution

x = {1.75, -2.307692308}

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