(4x-2)(x-3)=0

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Solution for (4x-2)(x-3)=0 equation:


Simplifying
(4x + -2)(x + -3) = 0

Reorder the terms:
(-2 + 4x)(x + -3) = 0

Reorder the terms:
(-2 + 4x)(-3 + x) = 0

Multiply (-2 + 4x) * (-3 + x)
(-2(-3 + x) + 4x * (-3 + x)) = 0
((-3 * -2 + x * -2) + 4x * (-3 + x)) = 0
((6 + -2x) + 4x * (-3 + x)) = 0
(6 + -2x + (-3 * 4x + x * 4x)) = 0
(6 + -2x + (-12x + 4x2)) = 0

Combine like terms: -2x + -12x = -14x
(6 + -14x + 4x2) = 0

Solving
6 + -14x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -7x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

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 = {0.5, 3}

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