(9x-5)(8x+6)=0

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Solution for (9x-5)(8x+6)=0 equation:


Simplifying
(9x + -5)(8x + 6) = 0

Reorder the terms:
(-5 + 9x)(8x + 6) = 0

Reorder the terms:
(-5 + 9x)(6 + 8x) = 0

Multiply (-5 + 9x) * (6 + 8x)
(-5(6 + 8x) + 9x * (6 + 8x)) = 0
((6 * -5 + 8x * -5) + 9x * (6 + 8x)) = 0
((-30 + -40x) + 9x * (6 + 8x)) = 0
(-30 + -40x + (6 * 9x + 8x * 9x)) = 0
(-30 + -40x + (54x + 72x2)) = 0

Combine like terms: -40x + 54x = 14x
(-30 + 14x + 72x2) = 0

Solving
-30 + 14x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 7x + 36x2) = 0

Factor a trinomial.
2((-3 + -4x)(5 + -9x)) = 0

Ignore the factor 2.

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 '(5 + -9x)' equal to zero and attempt to solve: Simplifying 5 + -9x = 0 Solving 5 + -9x = 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 + -9x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9x = 0 + -5 -9x = 0 + -5 Combine like terms: 0 + -5 = -5 -9x = -5 Divide each side by '-9'. x = 0.5555555556 Simplifying x = 0.5555555556

Solution

x = {-0.75, 0.5555555556}

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