2*(x+7)*3*(2x-5)=

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Solution for 2*(x+7)*3*(2x-5)= equation:


Simplifying
2(x + 7) * 3(2x + -5) = 0

Reorder the terms:
2(7 + x) * 3(2x + -5) = 0

Reorder the terms:
2(7 + x) * 3(-5 + 2x) = 0

Reorder the terms for easier multiplication:
2 * 3(7 + x)(-5 + 2x) = 0

Multiply 2 * 3
6(7 + x)(-5 + 2x) = 0

Multiply (7 + x) * (-5 + 2x)
6(7(-5 + 2x) + x(-5 + 2x)) = 0
6((-5 * 7 + 2x * 7) + x(-5 + 2x)) = 0
6((-35 + 14x) + x(-5 + 2x)) = 0
6(-35 + 14x + (-5 * x + 2x * x)) = 0
6(-35 + 14x + (-5x + 2x2)) = 0

Combine like terms: 14x + -5x = 9x
6(-35 + 9x + 2x2) = 0
(-35 * 6 + 9x * 6 + 2x2 * 6) = 0
(-210 + 54x + 12x2) = 0

Solving
-210 + 54x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-35 + 9x + 2x2) = 0

Factor a trinomial.
6((-7 + -1x)(5 + -2x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-7, 2.5}

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