0=5(4x-3)(x-50)

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Solution for 0=5(4x-3)(x-50) equation:


Simplifying
0 = 5(4x + -3)(x + -50)

Reorder the terms:
0 = 5(-3 + 4x)(x + -50)

Reorder the terms:
0 = 5(-3 + 4x)(-50 + x)

Multiply (-3 + 4x) * (-50 + x)
0 = 5(-3(-50 + x) + 4x * (-50 + x))
0 = 5((-50 * -3 + x * -3) + 4x * (-50 + x))
0 = 5((150 + -3x) + 4x * (-50 + x))
0 = 5(150 + -3x + (-50 * 4x + x * 4x))
0 = 5(150 + -3x + (-200x + 4x2))

Combine like terms: -3x + -200x = -203x
0 = 5(150 + -203x + 4x2)
0 = (150 * 5 + -203x * 5 + 4x2 * 5)
0 = (750 + -1015x + 20x2)

Solving
0 = 750 + -1015x + 20x2

Solving for variable 'x'.

Combine like terms: 0 + -750 = -750
-750 + 1015x + -20x2 = 750 + -1015x + 20x2 + -750 + 1015x + -20x2

Reorder the terms:
-750 + 1015x + -20x2 = 750 + -750 + -1015x + 1015x + 20x2 + -20x2

Combine like terms: 750 + -750 = 0
-750 + 1015x + -20x2 = 0 + -1015x + 1015x + 20x2 + -20x2
-750 + 1015x + -20x2 = -1015x + 1015x + 20x2 + -20x2

Combine like terms: -1015x + 1015x = 0
-750 + 1015x + -20x2 = 0 + 20x2 + -20x2
-750 + 1015x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-750 + 1015x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-150 + 203x + -4x2) = 0

Factor a trinomial.
5((-50 + x)(3 + -4x)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-50 + x)' equal to zero and attempt to solve: Simplifying -50 + x = 0 Solving -50 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + x = 0 + 50 x = 0 + 50 Combine like terms: 0 + 50 = 50 x = 50 Simplifying x = 50

Subproblem 2

Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75

Solution

x = {50, 0.75}

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