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

Subproblem 1

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

Subproblem 2

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

Solution

x = {-0.75, 1.333333333}

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