(3a-5)(4a-7)=

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Solution for (3a-5)(4a-7)= equation:


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

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

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

Multiply (-5 + 3a) * (-7 + 4a)
(-5(-7 + 4a) + 3a * (-7 + 4a)) = 0
((-7 * -5 + 4a * -5) + 3a * (-7 + 4a)) = 0
((35 + -20a) + 3a * (-7 + 4a)) = 0
(35 + -20a + (-7 * 3a + 4a * 3a)) = 0
(35 + -20a + (-21a + 12a2)) = 0

Combine like terms: -20a + -21a = -41a
(35 + -41a + 12a2) = 0

Solving
35 + -41a + 12a2 = 0

Solving for variable 'a'.

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

Subproblem 1

Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667

Subproblem 2

Set the factor '(7 + -4a)' equal to zero and attempt to solve: Simplifying 7 + -4a = 0 Solving 7 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4a = 0 + -7 -4a = 0 + -7 Combine like terms: 0 + -7 = -7 -4a = -7 Divide each side by '-4'. a = 1.75 Simplifying a = 1.75

Solution

a = {1.666666667, 1.75}

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