(4x-6)(5x-20)=0

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Solution for (4x-6)(5x-20)=0 equation:


Simplifying
(4x + -6)(5x + -20) = 0

Reorder the terms:
(-6 + 4x)(5x + -20) = 0

Reorder the terms:
(-6 + 4x)(-20 + 5x) = 0

Multiply (-6 + 4x) * (-20 + 5x)
(-6(-20 + 5x) + 4x * (-20 + 5x)) = 0
((-20 * -6 + 5x * -6) + 4x * (-20 + 5x)) = 0
((120 + -30x) + 4x * (-20 + 5x)) = 0
(120 + -30x + (-20 * 4x + 5x * 4x)) = 0
(120 + -30x + (-80x + 20x2)) = 0

Combine like terms: -30x + -80x = -110x
(120 + -110x + 20x2) = 0

Solving
120 + -110x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(12 + -11x + 2x2) = 0

Factor a trinomial.
10((3 + -2x)(4 + -1x)) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {1.5, 4}

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