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

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


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

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

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

Multiply (-5 + 2x) * (2 + 7x)
5(-5(2 + 7x) + 2x * (2 + 7x)) = 0
5((2 * -5 + 7x * -5) + 2x * (2 + 7x)) = 0
5((-10 + -35x) + 2x * (2 + 7x)) = 0
5(-10 + -35x + (2 * 2x + 7x * 2x)) = 0
5(-10 + -35x + (4x + 14x2)) = 0

Combine like terms: -35x + 4x = -31x
5(-10 + -31x + 14x2) = 0
(-10 * 5 + -31x * 5 + 14x2 * 5) = 0
(-50 + -155x + 70x2) = 0

Solving
-50 + -155x + 70x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + -31x + 14x2) = 0

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

Ignore the factor 5.

Subproblem 1

Set the factor '(-2 + -7x)' equal to zero and attempt to solve: Simplifying -2 + -7x = 0 Solving -2 + -7x = 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 + -7x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7x = 0 + 2 -7x = 0 + 2 Combine like terms: 0 + 2 = 2 -7x = 2 Divide each side by '-7'. x = -0.2857142857 Simplifying x = -0.2857142857

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-0.2857142857, 2.5}

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