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

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


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

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

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

Multiply (-4 + 5x) * (5 + x)
2(-4(5 + x) + 5x * (5 + x)) = 0
2((5 * -4 + x * -4) + 5x * (5 + x)) = 0
2((-20 + -4x) + 5x * (5 + x)) = 0
2(-20 + -4x + (5 * 5x + x * 5x)) = 0
2(-20 + -4x + (25x + 5x2)) = 0

Combine like terms: -4x + 25x = 21x
2(-20 + 21x + 5x2) = 0
(-20 * 2 + 21x * 2 + 5x2 * 2) = 0
(-40 + 42x + 10x2) = 0

Solving
-40 + 42x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 21x + 5x2) = 0

Factor a trinomial.
2((-5 + -1x)(4 + -5x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 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 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8

Solution

x = {-5, 0.8}

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