5(x+1)(4x-1)=0

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Solution for 5(x+1)(4x-1)=0 equation:


Simplifying
5(x + 1)(4x + -1) = 0

Reorder the terms:
5(1 + x)(4x + -1) = 0

Reorder the terms:
5(1 + x)(-1 + 4x) = 0

Multiply (1 + x) * (-1 + 4x)
5(1(-1 + 4x) + x(-1 + 4x)) = 0
5((-1 * 1 + 4x * 1) + x(-1 + 4x)) = 0
5((-1 + 4x) + x(-1 + 4x)) = 0
5(-1 + 4x + (-1 * x + 4x * x)) = 0
5(-1 + 4x + (-1x + 4x2)) = 0

Combine like terms: 4x + -1x = 3x
5(-1 + 3x + 4x2) = 0
(-1 * 5 + 3x * 5 + 4x2 * 5) = 0
(-5 + 15x + 20x2) = 0

Solving
-5 + 15x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 3x + 4x2) = 0

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

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25

Solution

x = {-1, 0.25}

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