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

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


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

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

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

Multiply (4 + 7x) * (-5 + 3x)
(4(-5 + 3x) + 7x * (-5 + 3x)) = 0
((-5 * 4 + 3x * 4) + 7x * (-5 + 3x)) = 0
((-20 + 12x) + 7x * (-5 + 3x)) = 0
(-20 + 12x + (-5 * 7x + 3x * 7x)) = 0
(-20 + 12x + (-35x + 21x2)) = 0

Combine like terms: 12x + -35x = -23x
(-20 + -23x + 21x2) = 0

Solving
-20 + -23x + 21x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-4 + -7x)' equal to zero and attempt to solve: Simplifying -4 + -7x = 0 Solving -4 + -7x = 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 + -7x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7x = 0 + 4 -7x = 0 + 4 Combine like terms: 0 + 4 = 4 -7x = 4 Divide each side by '-7'. x = -0.5714285714 Simplifying x = -0.5714285714

Subproblem 2

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

Solution

x = {-0.5714285714, 1.666666667}

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