(3k+4)(5k-7)=0

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


Simplifying
(3k + 4)(5k + -7) = 0

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

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

Multiply (4 + 3k) * (-7 + 5k)
(4(-7 + 5k) + 3k * (-7 + 5k)) = 0
((-7 * 4 + 5k * 4) + 3k * (-7 + 5k)) = 0
((-28 + 20k) + 3k * (-7 + 5k)) = 0
(-28 + 20k + (-7 * 3k + 5k * 3k)) = 0
(-28 + 20k + (-21k + 15k2)) = 0

Combine like terms: 20k + -21k = -1k
(-28 + -1k + 15k2) = 0

Solving
-28 + -1k + 15k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-4 + -3k)(7 + -5k) = 0


Subproblem 1
Set the factor '(-4 + -3k)' equal to zero and attempt to solve:

Simplifying
-4 + -3k = 0

Solving
-4 + -3k = 0

Move all terms containing k to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3k = 0 + 4
-3k = 0 + 4

Combine like terms: 0 + 4 = 4
-3k = 4

Divide each side by '-3'.
k = -1.333333333

Simplifying
k = -1.333333333

Subproblem 2
Set the factor '(7 + -5k)' equal to zero and attempt to solve:

Simplifying
7 + -5k = 0

Solving
7 + -5k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -5k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5k = 0 + -7
-5k = 0 + -7

Combine like terms: 0 + -7 = -7
-5k = -7

Divide each side by '-5'.
k = 1.4

Simplifying
k = 1.4
Solution
k = {-1.333333333, 1.4}

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