(7x-5)(2x+4)=0

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Solution for (7x-5)(2x+4)=0 equation:


Simplifying
(7x + -5)(2x + 4) = 0

Reorder the terms:
(-5 + 7x)(2x + 4) = 0

Reorder the terms:
(-5 + 7x)(4 + 2x) = 0

Multiply (-5 + 7x) * (4 + 2x)
(-5(4 + 2x) + 7x * (4 + 2x)) = 0
((4 * -5 + 2x * -5) + 7x * (4 + 2x)) = 0
((-20 + -10x) + 7x * (4 + 2x)) = 0
(-20 + -10x + (4 * 7x + 2x * 7x)) = 0
(-20 + -10x + (28x + 14x2)) = 0

Combine like terms: -10x + 28x = 18x
(-20 + 18x + 14x2) = 0

Solving
-20 + 18x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 9x + 7x2) = 0

Factor a trinomial.
2((-2 + -1x)(5 + -7x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 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 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143

Solution

x = {-2, 0.7142857143}

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