(x-7)*(x-10)=0

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Solution for (x-7)*(x-10)=0 equation:


Simplifying
(x + -7)(x + -10) = 0

Reorder the terms:
(-7 + x)(x + -10) = 0

Reorder the terms:
(-7 + x)(-10 + x) = 0

Multiply (-7 + x) * (-10 + x)
(-7(-10 + x) + x(-10 + x)) = 0
((-10 * -7 + x * -7) + x(-10 + x)) = 0
((70 + -7x) + x(-10 + x)) = 0
(70 + -7x + (-10 * x + x * x)) = 0
(70 + -7x + (-10x + x2)) = 0

Combine like terms: -7x + -10x = -17x
(70 + -17x + x2) = 0

Solving
70 + -17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -1x)(10 + -1x) = 0

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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {7, 10}

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