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

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Solution for 2(x-6)(4x-5)=0 equation:


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

Reorder the terms:
2(-6 + x)(4x + -5) = 0

Reorder the terms:
2(-6 + x)(-5 + 4x) = 0

Multiply (-6 + x) * (-5 + 4x)
2(-6(-5 + 4x) + x(-5 + 4x)) = 0
2((-5 * -6 + 4x * -6) + x(-5 + 4x)) = 0
2((30 + -24x) + x(-5 + 4x)) = 0
2(30 + -24x + (-5 * x + 4x * x)) = 0
2(30 + -24x + (-5x + 4x2)) = 0

Combine like terms: -24x + -5x = -29x
2(30 + -29x + 4x2) = 0
(30 * 2 + -29x * 2 + 4x2 * 2) = 0
(60 + -58x + 8x2) = 0

Solving
60 + -58x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -29x + 4x2) = 0

Factor a trinomial.
2((5 + -4x)(6 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {1.25, 6}

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