(3x+4)(4x-3)=0

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


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

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

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

Multiply (4 + 3x) * (-3 + 4x)
(4(-3 + 4x) + 3x * (-3 + 4x)) = 0
((-3 * 4 + 4x * 4) + 3x * (-3 + 4x)) = 0
((-12 + 16x) + 3x * (-3 + 4x)) = 0
(-12 + 16x + (-3 * 3x + 4x * 3x)) = 0
(-12 + 16x + (-9x + 12x2)) = 0

Combine like terms: 16x + -9x = 7x
(-12 + 7x + 12x2) = 0

Solving
-12 + 7x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(3 + -4x) = 0

Subproblem 1

Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333

Subproblem 2

Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75

Solution

x = {-1.333333333, 0.75}

 

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