(x+10)(2x-3)=(2x)(2x)

Solution for (x+10)(2x-3)=(2x)(2x) equation:

Simplifying
(x + 10)(2x + -3) = (2x)(2x)

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

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

Multiply (10 + x) * (-3 + 2x)
(10(-3 + 2x) + x(-3 + 2x)) = (2x)(2x)
((-3 * 10 + 2x * 10) + x(-3 + 2x)) = (2x)(2x)
((-30 + 20x) + x(-3 + 2x)) = (2x)(2x)
(-30 + 20x + (-3 * x + 2x * x)) = (2x)(2x)
(-30 + 20x + (-3x + 2x2)) = (2x)(2x)

Combine like terms: 20x + -3x = 17x
(-30 + 17x + 2x2) = (2x)(2x)

Remove parenthesis around (2x)
-30 + 17x + 2x2 = 2x(2x)

Remove parenthesis around (2x)
-30 + 17x + 2x2 = 2x * 2x

Reorder the terms for easier multiplication:
-30 + 17x + 2x2 = 2 * 2x * x

Multiply 2 * 2
-30 + 17x + 2x2 = 4x * x

Multiply x * x
-30 + 17x + 2x2 = 4x2

Solving
-30 + 17x + 2x2 = 4x2

Solving for variable 'x'.

Combine like terms: 2x2 + -4x2 = -2x2
-30 + 17x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-30 + 17x + -2x2 = 0

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

Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 2.5}