5(x-3)(4x+1)=0

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Solution for 5(x-3)(4x+1)=0 equation:


Simplifying
5(x + -3)(4x + 1) = 0

Reorder the terms:
5(-3 + x)(4x + 1) = 0

Reorder the terms:
5(-3 + x)(1 + 4x) = 0

Multiply (-3 + x) * (1 + 4x)
5(-3(1 + 4x) + x(1 + 4x)) = 0
5((1 * -3 + 4x * -3) + x(1 + 4x)) = 0
5((-3 + -12x) + x(1 + 4x)) = 0
5(-3 + -12x + (1 * x + 4x * x)) = 0
5(-3 + -12x + (1x + 4x2)) = 0

Combine like terms: -12x + 1x = -11x
5(-3 + -11x + 4x2) = 0
(-3 * 5 + -11x * 5 + 4x2 * 5) = 0
(-15 + -55x + 20x2) = 0

Solving
-15 + -55x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -11x + 4x2) = 0

Factor a trinomial.
5((-1 + -4x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-0.25, 3}

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